(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 7.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[    185103,       4974]
NotebookOptionsPosition[    154927,       4216]
NotebookOutlinePosition[    172378,       4540]
CellTagsIndexPosition[    172162,       4532]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[TextData[StyleBox["Tema 5:\n Resoluci\[OAcute]n de Ecuaciones e \
Inecuaciones.", "Title"]], "Subtitle",
 CellChangeTimes->{
  3.427102646578125*^9, 3.427517205850881*^9, {3.4281289774375*^9, 
   3.428128984421875*^9}, {3.459150319*^9, 3.45915032721875*^9}, {
   3.459666793890625*^9, 3.45966681515625*^9}},
 TextAlignment->Center,
 TextJustification->0],

Cell[CellGroupData[{

Cell["Soluciones exactas y aproximadas de ecuaciones", "Section 1",
 CellChangeTimes->{{3.459151685328125*^9, 3.459151685671875*^9}}],

Cell[TextData[{
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " nos permite obtener la soluci\[OAcute]n exacta de muchas ecuaciones y \
sistemas de ecuaciones incluyendo las polin\[OAcute]micas de grado 4 o menor \
con el comando ",
 StyleBox["Solve",
  FontSlant->"Italic"],
 ". La igualdad l\[OAcute]gica viene representada por == (dos iguales \
seguidos). A continuaci\[OAcute]n vamos a obtener informaci\[OAcute]n sobre \
este s\[IAcute]mbolo y el comando ",
 StyleBox["Solve . ",
  FontSlant->"Italic"]
}], "Text",
 CellChangeTimes->{{3.45915170225*^9, 3.4591517100625*^9}},
 TextAlignment->Left,
 TextJustification->1],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"?", "=="}]], "Input"],

Cell[BoxData[
 RowBox[{
  StyleBox["\<\"\!\(\*RowBox[{StyleBox[\\\"lhs\\\", \\\"TI\\\"], \\\"==\\\", \
StyleBox[\\\"rhs\\\", \\\"TI\\\"]}]\) returns True if \
\!\(\*StyleBox[\\\"lhs\\\", \\\"TI\\\"]\) and \!\(\*StyleBox[\\\"rhs\\\", \
\\\"TI\\\"]\) are identical. \"\>", "MSG"], "\[NonBreakingSpace]", 
  ButtonBox[
   StyleBox["\[RightSkeleton]", "SR"],
   Active->True,
   BaseStyle->"Link",
   ButtonData->"paclet:ref/Equal"]}]], "Print", "PrintUsage",
 CellChangeTimes->{3.469795180671875*^9},
 CellTags->"Info3469798779-9406029"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"?", "Solve"}]], "Input"],

Cell[BoxData[
 RowBox[{
  StyleBox["\<\"\!\(\*RowBox[{\\\"Solve\\\", \\\"[\\\", \
RowBox[{StyleBox[\\\"eqns\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"vars\\\", \
\\\"TI\\\"]}], \\\"]\\\"}]\) attempts to solve an equation or set of \
equations for the variables \!\(\*StyleBox[\\\"vars\\\", \\\"TI\\\"]\). \\n\!\
\(\*RowBox[{\\\"Solve\\\", \\\"[\\\", RowBox[{StyleBox[\\\"eqns\\\", \\\"TI\\\
\"], \\\",\\\", StyleBox[\\\"vars\\\", \\\"TI\\\"], \\\",\\\", \
StyleBox[\\\"elims\\\", \\\"TI\\\"]}], \\\"]\\\"}]\) attempts to solve the \
equations for \!\(\*StyleBox[\\\"vars\\\", \\\"TI\\\"]\), eliminating the \
variables \!\(\*StyleBox[\\\"elims\\\", \\\"TI\\\"]\). \"\>", "MSG"], 
  "\[NonBreakingSpace]", 
  ButtonBox[
   StyleBox["\[RightSkeleton]", "SR"],
   Active->True,
   BaseStyle->"Link",
   ButtonData->"paclet:ref/Solve"]}]], "Print", "PrintUsage",
 CellChangeTimes->{3.46979518090625*^9},
 CellTags->"Info3469798780-6240857"]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo 1\nResolver las ecuaciones:\na) 5x+2=-3.\nb) ",
 Cell[BoxData[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["x", "2"], "+", 
     RowBox[{"3", "x"}], "+", "2"}], 
    RowBox[{"x", "+", "2"}]], "=", "0"}]]],
 ".\nc) ",
 Cell[BoxData[
  RowBox[{
   RowBox[{
    SuperscriptBox["x", "3"], "-", 
    SuperscriptBox["x", "2"], "+", "2"}], "=", "0"}]]]
}], "Subsection",
 CellChangeTimes->{{3.457929362078125*^9, 3.45792939415625*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"5", "x"}], "+", "2"}], "\[Equal]", 
   RowBox[{"-", "3"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.45792914503125*^9, 3.45792917315625*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"x", "\[Rule]", 
    RowBox[{"-", "1"}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.461566835484375*^9, 3.469795181*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["x", "2"], "+", 
     RowBox[{"3", "x"}], "+", "2"}], 
    RowBox[{"x", "+", "2"}]], "==", "0"}], "]"}]], "Input",
 CellChangeTimes->{{3.457929202328125*^9, 3.457929241578125*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"x", "\[Rule]", 
    RowBox[{"-", "1"}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.46156683603125*^9, 3.4697951810625*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    SuperscriptBox["x", "3"], "-", 
    SuperscriptBox["x", "2"], "+", "2"}], "==", "0"}], "]"}]], "Input",
 CellChangeTimes->{{3.457929321546875*^9, 3.4579293480625*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"-", "1"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"1", "-", "\[ImaginaryI]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"1", "+", "\[ImaginaryI]"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.461566836359375*^9, 3.469795181109375*^9}]
}, Open  ]],

Cell[TextData[{
 "La salida que devuelve Mathematica no es uno  o varios n\[UAcute]meros sino \
una lista en la que se da el valor que habr\[IAcute]a que asignar a x para \
obtener la soluci\[OAcute]n de la ecuaci\[OAcute]n. Para obtener el \
n\[UAcute]mero hay que utilizar el ",
 StyleBox["operador reemplazamiento, /.",
  FontWeight->"Bold"],
 ". En primer lugar",
 StyleBox[" ",
  FontWeight->"Bold"],
 "se guarda el resultado del comando Solve en una variable, por ejemplo s1. \
Despu\[EAcute]s tecleamos la variable que est\[AAcute] delante de la flecha \
en s1, el operador reemplazamiento y el elemento de la lista s1 en el que se \
encuentra el valor num\[EAcute]rico.\nLas siguientes entradas muestran dos \
casos distintos, el primero con una \[UAcute]nica soluci\[OAcute]n y el \
segundo con varias."
}], "Text",
 CellChangeTimes->{{3.427518123285643*^9, 3.427518162364581*^9}, {
  3.45915173184375*^9, 3.459151796625*^9}, {3.459151860859375*^9, 
  3.459152055859375*^9}},
 TextAlignment->Left,
 TextJustification->1],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"s1", "=", 
  RowBox[{"Solve", "[", 
   RowBox[{
    FractionBox[
     RowBox[{
      SuperscriptBox["x", "2"], "+", 
      RowBox[{"3", "x"}], "+", "2"}], 
     RowBox[{"x", "+", "2"}]], "==", "0"}], "]"}]}]], "Input",
 CellChangeTimes->{3.457929408078125*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"x", "\[Rule]", 
    RowBox[{"-", "1"}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.459151833265625*^9, 3.461566836375*^9, 
  3.46979518115625*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"x", "/.", 
  RowBox[{"s1", "[", 
   RowBox[{"[", "1", "]"}], "]"}]}]], "Input",
 CellChangeTimes->{3.45792942475*^9, 3.45915192275*^9}],

Cell[BoxData[
 RowBox[{"-", "1"}]], "Output",
 CellChangeTimes->{3.459152060703125*^9, 3.461566836375*^9, 
  3.469795181203125*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"s2", "=", 
  RowBox[{"Solve", "[", 
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "3"], "-", 
     SuperscriptBox["x", "2"], "+", "2"}], "==", "0"}], "]"}]}]], "Input",
 CellChangeTimes->{3.4579294529375*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"-", "1"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"1", "-", "\[ImaginaryI]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"1", "+", "\[ImaginaryI]"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.459152062328125*^9, 3.461566836390625*^9, 
  3.469795181234375*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"x1", "=", 
  RowBox[{"x", "/.", 
   RowBox[{"s2", "[", 
    RowBox[{"[", "1", "]"}], "]"}]}]}]], "Input"],

Cell[BoxData[
 RowBox[{"-", "1"}]], "Output",
 CellChangeTimes->{3.459152065265625*^9, 3.461566836390625*^9, 
  3.469795181265625*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"x2", "=", 
  RowBox[{"x", "/.", 
   RowBox[{"s2", "[", 
    RowBox[{"[", "2", "]"}], "]"}]}]}]], "Input"],

Cell[BoxData[
 RowBox[{"1", "-", "\[ImaginaryI]"}]], "Output",
 CellChangeTimes->{3.45915206634375*^9, 3.461566836390625*^9, 
  3.4697951813125*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"x3", "=", 
  RowBox[{"x", "/.", 
   RowBox[{"s2", "[", 
    RowBox[{"[", "3", "]"}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.45792946490625*^9, 3.457929470140625*^9}}],

Cell[BoxData[
 RowBox[{"1", "+", "\[ImaginaryI]"}]], "Output",
 CellChangeTimes->{3.459152067046875*^9, 3.46156683640625*^9, 
  3.46979518134375*^9}]
}, Open  ]],

Cell[TextData[{
 "Es importante tener en cuenta que una ecuaci\[OAcute]n como:\n\tsin(x)=a\n\
tiene infinitas soluciones. Al resolver este tipo de ecuaciones ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " necesita utilizar funciones inversas y presenta una soluci\[OAcute]n de \
las posibles y un mensaje indicando que hay m\[AAcute]s soluciones. "
}], "Text",
 CellChangeTimes->{{3.427518087015765*^9, 3.427518092286549*^9}, {
  3.427518392570492*^9, 3.4275185523611298`*^9}},
 TextAlignment->Left,
 TextJustification->1],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"Sin", "[", "x", "]"}], "\[Equal]", ".5"}], ",", "x"}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.459152078546875*^9, 3.459152092609375*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"Solve", "::", "\<\"ifun\"\>"}], 
  RowBox[{
  ":", " "}], "\<\"\\!\\(\\*StyleBox[\\\"\\\\\\\"Inverse functions are being \
used by \\\\\\\"\\\", \
\\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\!\\(Solve\\), \\\"MT\\\"]\\)\
\[NoBreak]\\!\\(\\*StyleBox[\\\"\\\\\\\", so some solutions may not be found; \
use Reduce for complete solution information.\\\\\\\"\\\", \\\"MT\\\"]\\) \\!\
\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \
ButtonFrame->None, ButtonData:>\\\"paclet:ref/Solve\\\", ButtonNote -> \
\\\"Solve::ifun\\\"]\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.45915209375*^9, 3.4615668366875*^9, 3.469795181421875*^9}
  ],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"x", "\[Rule]", "0.5235987755982989`"}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.45915209375*^9, 3.461566836703125*^9, 
  3.469795181453125*^9}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo 2\nHallar una soluci\[OAcute]n de la ecuaci\[OAcute]n: ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     RowBox[{"Cos", "(", "x", ")"}], "-", 
     RowBox[{"2", 
      RowBox[{"Sen", "(", 
       RowBox[{"2", "x"}], ")"}]}]}], " ", "=", " ", "0"}], TraditionalForm]]]
}], "Subsection",
 CellChangeTimes->{{3.4579295895*^9, 3.4579296050625*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"Cos", "[", "x", "]"}], "-", 
     RowBox[{"2", " ", 
      RowBox[{"Sin", "[", 
       RowBox[{"2", "x"}], "]"}]}]}], "==", "0"}], ",", "x"}], "]"}]], "Input",
 CellChangeTimes->{{3.457929481953125*^9, 3.4579295766875*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"Solve", "::", "\<\"ifun\"\>"}], 
  RowBox[{
  ":", " "}], "\<\"\\!\\(\\*StyleBox[\\\"\\\\\\\"Inverse functions are being \
used by \\\\\\\"\\\", \
\\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\!\\(Solve\\), \\\"MT\\\"]\\)\
\[NoBreak]\\!\\(\\*StyleBox[\\\"\\\\\\\", so some solutions may not be found; \
use Reduce for complete solution information.\\\\\\\"\\\", \\\"MT\\\"]\\) \\!\
\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \
ButtonFrame->None, ButtonData:>\\\"paclet:ref/Solve\\\", ButtonNote -> \
\\\"Solve::ifun\\\"]\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.461566836765625*^9, 3.469795181515625*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"-", 
      FractionBox["\[Pi]", "2"]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     FractionBox["\[Pi]", "2"]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"ArcSin", "[", 
      FractionBox["1", "4"], "]"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.461566836765625*^9, 3.46979518153125*^9}]
}, Open  ]],

Cell[TextData[{
 "\nCon el comando Solve se pueden resolver tambi\[EAcute]n sistemas de \
ecuaciones, que deber\[AAcute]n ir entre llaves. Si no se especifica nada m\
\[AAcute]s ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " intentar\[AAcute] resolver en todas las variables que aparezcan, pero se \
puede indicar tambi\[EAcute]n en qu\[EAcute] variables se desea la soluci\
\[OAcute]n, encerr\[AAcute]ndolas tambi\[EAcute]n entre llaves.\nDel mismo \
modo que en caso de una \[UAcute]nica ecuaci\[OAcute]n, se puede poner un \
nombre a la soluci\[OAcute]n del sistema que da ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " y utilizar este nombre y el operador reemplazamiento /. .\nSi ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " devuelve como soluci\[OAcute]n : { }(conjunto vacio) esto indica que el \
sistema no tiene soluci\[OAcute]n, es decir, que es incompatible."
}], "Text",
 CellChangeTimes->{{3.427518599312585*^9, 3.427518600356352*^9}, 
   3.457931466421875*^9, 3.4591521110625*^9},
 TextAlignment->Left,
 TextJustification->1]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo 3\nResolver los sistemas:\na) ",
 Cell[BoxData[
  RowBox[{
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "2"], "-", 
     RowBox[{"2", "x"}], "-", "y", "+", "1"}], "=", "0"}], ",", 
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "2"], "+", 
     RowBox[{"2", 
      SuperscriptBox["y", "2"]}]}], "=", "2"}]}]]],
 " .\nb) ",
 Cell[BoxData[
  RowBox[{
   RowBox[{
    RowBox[{
     FractionBox[
      SuperscriptBox["x", "2"], "4"], "-", 
     FractionBox[
      SuperscriptBox["y", "2"], "16"]}], "=", "1"}], ",", 
   RowBox[{"y", "=", "kx"}]}]]],
 " ."
}], "Subsection",
 CellChangeTimes->{{3.45792968884375*^9, 3.457929726125*^9}, {
  3.4591521940625*^9, 3.4591522218125*^9}, {3.45915238996875*^9, 
  3.459152391*^9}, {3.459152624390625*^9, 3.459152633640625*^9}}],

Cell[CellGroupData[{

Cell["a)", "Subsubsection",
 CellChangeTimes->{{3.4591527520625*^9, 3.45915275321875*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Solve", "[", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{
       SuperscriptBox["x", "2"], "-", 
       RowBox[{"2", "x"}], "-", "y", "+", "1"}], "\[Equal]", "0"}], ",", 
     RowBox[{
      RowBox[{
       SuperscriptBox["x", "2"], "+", 
       RowBox[{"2", 
        SuperscriptBox["y", "2"]}]}], "\[Equal]", "2"}]}], "}"}], "]"}], "//",
   "N"}]], "Input",
 CellChangeTimes->{{3.4579297399375*^9, 3.457929772328125*^9}, {
  3.459152167546875*^9, 3.4591521844375*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"y", "\[Rule]", "1.`"}], ",", 
     RowBox[{"x", "\[Rule]", "0.`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"y", "\[Rule]", "0.15729810613837605`"}], ",", 
     RowBox[{"x", "\[Rule]", "1.3966082527360921`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"y", "\[Rule]", 
      RowBox[{
       RowBox[{"-", "1.0786490530691877`"}], "-", 
       RowBox[{"0.6525757632523721`", " ", "\[ImaginaryI]"}]}]}], ",", 
     RowBox[{"x", "\[Rule]", 
      RowBox[{"1.301695873631954`", "\[InvisibleSpace]", "-", 
       RowBox[{"1.0815125765499614`", " ", "\[ImaginaryI]"}]}]}]}], "}"}], 
   ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"y", "\[Rule]", 
      RowBox[{
       RowBox[{"-", "1.0786490530691877`"}], "+", 
       RowBox[{"0.6525757632523721`", " ", "\[ImaginaryI]"}]}]}], ",", 
     RowBox[{"x", "\[Rule]", 
      RowBox[{"1.301695873631954`", "\[InvisibleSpace]", "+", 
       RowBox[{"1.0815125765499614`", " ", "\[ImaginaryI]"}]}]}]}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.459152186*^9, 3.4615668370625*^9, 3.469795181625*^9}]
}, Open  ]],

Cell["\<\
De las cuatro soluciones que se obtienen s\[OAcute]lamente las dos primeras \
corresponden a valores reales. Vamos a comprobar gr\[AAcute]ficamente que las \
dos curvas se cortan en los dos puntos correspondientes a las dos primeras \
raices.\
\>", "Text",
 CellChangeTimes->{{3.45915225303125*^9, 3.459152331109375*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ContourPlot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{
       SuperscriptBox["x", "2"], "-", 
       RowBox[{"2", "x"}], "-", "y", "+", "1"}], "\[Equal]", "0"}], ",", 
     RowBox[{
      RowBox[{
       SuperscriptBox["x", "2"], "+", 
       RowBox[{"2", 
        SuperscriptBox["y", "2"]}]}], "\[Equal]", "2"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"y", ",", 
     RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", 
   RowBox[{"Axes", "\[Rule]", "True"}], ",", 
   RowBox[{"Frame", "\[Rule]", "None"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.45793006015625*^9, 3.45793012515625*^9}, {
  3.45915223184375*^9, 3.459152236296875*^9}}],

Cell[BoxData[
 GraphicsBox[GraphicsComplexBox[CompressedData["
1:eJxdmAlYjWkbx48MaiTUmGxDYpRCtkGW7gghaWF8xpUZypYYaZpmzPd9w0Rh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   "], {{}, {}, 
    {Hue[0.67, 0.6, 0.6], 
     LineBox[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 
      19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 
      37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 
      55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 
      73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 
      91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 
      107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117}]}, 
    {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJwt0lN7FgAAgNFvYXlr2bVs27WwamnZPf2Ausu2rVVr2bZt27Ztn4suzi94
3/Au3aK7BgUCgZd0pwc96UVv+tCXfvRnAAMZxGCGMJRhDGcEIxnFaMYwlnGM
ZwITmcRkpjCVaUxnBjOJYRazmUMsc4ljHvNZwEIWsZglLGUZy1nBSlaxmjWs
ZR3r2cBGNrGZLWxlG9vZwU52sZs97GUf+znAQQ5xmCMc5RjHOcFJTnGaM5zl
HOe5wEUucZkrXOUa17nBTW5xmzvc5R73ecBDHvGYJzzlGc958b/rK17zhre8
4z0f+MgnPvOFr3zjOz/4yS9+84e/BAwTRDzik4CEBJOIxCQhKclITgpCCCUl
YaQiNWlISzrSk4GMZCIzWchKNrKTg3Bykovc5CEv+chPAQpSiMIUoSjFKE4J
SlKK0pShLOUoTwUqUonKVKEq1ahODWoSQS1qU4e6RFKP+jQgioY0ojFNaEo0
zWhOC1rSita0oS3taE8HOtKJzvwDhll5uQ==
      "]]}}],
  AspectRatio->1,
  Axes->True,
  Frame->None,
  PlotRange->{{-2, 2}, {-2, 2}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.459152238625*^9, 3.46156683709375*^9, 3.4697951816875*^9}
  ]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["b)", "Subsubsection",
 CellChangeTimes->{{3.45915277125*^9, 3.459152771953125*^9}}],

Cell["\<\
En el resultado del comando Solve vemos que para que la recta corte a la hip\
\[EAcute]rbola es necesario que el valor de k este comprendido entre - 2 y 2.
Esto se puede comprobar gr\[AAcute]ficamente utilizando el comando Manipulate.\
\>", "Text",
 CellChangeTimes->{{3.459152792390625*^9, 3.4591528760625*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{
       FractionBox[
        SuperscriptBox["x", "2"], "4"], "-", 
       FractionBox[
        SuperscriptBox["y", "2"], "16"]}], "==", "1"}], ",", 
     RowBox[{"y", "\[Equal]", 
      RowBox[{"k", "*", "x"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.459152347890625*^9, 3.4591523555625*^9}, 
   3.459152386296875*^9, {3.459152641125*^9, 3.4591526455625*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"y", "\[Rule]", 
      RowBox[{"-", 
       FractionBox[
        RowBox[{"4", " ", "k"}], 
        SqrtBox[
         RowBox[{"4", "-", 
          SuperscriptBox["k", "2"]}]]]}]}], ",", 
     RowBox[{"x", "\[Rule]", 
      RowBox[{"-", 
       FractionBox["4", 
        SqrtBox[
         RowBox[{"4", "-", 
          SuperscriptBox["k", "2"]}]]]}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"y", "\[Rule]", 
      FractionBox[
       RowBox[{"4", " ", "k"}], 
       SqrtBox[
        RowBox[{"4", "-", 
         SuperscriptBox["k", "2"]}]]]}], ",", 
     RowBox[{"x", "\[Rule]", 
      FractionBox["4", 
       SqrtBox[
        RowBox[{"4", "-", 
         SuperscriptBox["k", "2"]}]]]}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.459152358609375*^9, 3.459152394640625*^9}, 
   3.4591526465*^9, 3.461566837109375*^9, 3.46979518171875*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"ContourPlot", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{
        RowBox[{
         FractionBox[
          SuperscriptBox["x", "2"], "4"], "-", 
         FractionBox[
          SuperscriptBox["y", "2"], "16"]}], "==", "1"}], ",", 
       RowBox[{"y", "\[Equal]", 
        RowBox[{"k", "*", "x"}]}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "4"}], ",", "4"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "4"}], ",", "4"}], "}"}], ",", 
     RowBox[{"Axes", "\[Rule]", "True"}], ",", 
     RowBox[{"Frame", "\[Rule]", "None"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"k", ",", 
     RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.45793015271875*^9, 3.45793020659375*^9}, {
  3.4579302485625*^9, 3.457930292953125*^9}, {3.45915240790625*^9, 
  3.459152450421875*^9}, {3.459152667078125*^9, 3.459152709328125*^9}}],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`k$$ = -2., Typeset`show$$ = True, 
    Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{
      Hold[$CellContext`k$$], -2, 2}}, Typeset`size$$ = {540., {265., 275.}}, 
    Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = 
    True, $CellContext`k$284$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, "Variables" :> {$CellContext`k$$ = -2}, 
      "ControllerVariables" :> {
        Hold[$CellContext`k$$, $CellContext`k$284$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> 
      ContourPlot[{$CellContext`x^2/4 - $CellContext`y^2/16 == 
         1, $CellContext`y == $CellContext`k$$ $CellContext`x}, \
{$CellContext`x, -4, 4}, {$CellContext`y, -4, 4}, Axes -> True, Frame -> 
        None], "Specifications" :> {{$CellContext`k$$, -2, 2}}, 
      "Options" :> {}, "DefaultOptions" :> {}],
     ImageSizeCache->{605., {331., 338.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    SynchronousInitialization->True,
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{{3.459152424921875*^9, 3.45915245284375*^9}, {
   3.45915271096875*^9, 3.45915274009375*^9}, 3.461566837125*^9, 
   3.469795181765625*^9}]
}, Open  ]],

Cell[TextData[{
 StyleBox["\nMathematica",
  FontSlant->"Italic"],
 " puede obtener la soluci\[OAcute]n exacta de cualquier ecuaci\[OAcute]n \
polin\[OAcute]mica de grado 4 o menor, aunque, en muchos casos dicha soluci\
\[OAcute]n no tendr\[AAcute] mucho sentido y es prefereible obtener un valor \
aproximado con el comando N[expresi\[OAcute]n] , //N o mediante el comando \
NSolve.\nPara ecuaciones polin\[OAcute]micas de grado mayor que 4 no existen, \
en general, f\[OAcute]rmulas expl\[IAcute]citas. En muchas ocasiones la \
respuesta de ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " es un objeto del tipo Root"
}], "Text",
 CellChangeTimes->{{3.42710257325*^9, 3.427102574828125*^9}, {
  3.427518634426188*^9, 3.4275186373001423`*^9}, {3.427518698628183*^9, 
  3.427518701380021*^9}, {3.427518735880746*^9, 3.4275188057047987`*^9}, {
  3.45915288140625*^9, 3.459152904828125*^9}},
 TextAlignment->Left,
 TextJustification->1],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "7"}], "-", 
     RowBox[{"2", 
      SuperscriptBox["x", "4"]}], "+", "11"}], "==", "0"}], ",", "x"}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.45792982875*^9, 3.45792985246875*^9}},
 CellID->1497],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"Root", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"11", "-", 
         RowBox[{"2", " ", 
          SuperscriptBox["#1", "4"]}], "+", 
         SuperscriptBox["#1", "7"]}], "&"}], ",", "1"}], "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"Root", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"11", "-", 
         RowBox[{"2", " ", 
          SuperscriptBox["#1", "4"]}], "+", 
         SuperscriptBox["#1", "7"]}], "&"}], ",", "2"}], "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"Root", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"11", "-", 
         RowBox[{"2", " ", 
          SuperscriptBox["#1", "4"]}], "+", 
         SuperscriptBox["#1", "7"]}], "&"}], ",", "3"}], "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"Root", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"11", "-", 
         RowBox[{"2", " ", 
          SuperscriptBox["#1", "4"]}], "+", 
         SuperscriptBox["#1", "7"]}], "&"}], ",", "4"}], "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"Root", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"11", "-", 
         RowBox[{"2", " ", 
          SuperscriptBox["#1", "4"]}], "+", 
         SuperscriptBox["#1", "7"]}], "&"}], ",", "5"}], "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"Root", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"11", "-", 
         RowBox[{"2", " ", 
          SuperscriptBox["#1", "4"]}], "+", 
         SuperscriptBox["#1", "7"]}], "&"}], ",", "6"}], "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"Root", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"11", "-", 
         RowBox[{"2", " ", 
          SuperscriptBox["#1", "4"]}], "+", 
         SuperscriptBox["#1", "7"]}], "&"}], ",", "7"}], "]"}]}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.459152912515625*^9, 3.4615668373125*^9, 
  3.469795181890625*^9}]
}, Open  ]],

Cell["\<\
Esta respuesta es una representaci\[OAcute]n simb\[OAcute]lica \
impl\[IAcute]cita. Sin embargo se puede obtener la soluci\[OAcute]n \
aproximada con el comando NSolve o poniendo // N al final del comando \
anterior.\
\>", "Text",
 CellChangeTimes->{{3.427519010186162*^9, 3.427519125757452*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"NSolve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "7"}], "-", 
     RowBox[{"2", 
      SuperscriptBox["x", "4"]}], "+", "11"}], "==", "0"}], ",", "x"}], 
  "]"}]], "Input",
 CellChangeTimes->{3.42751914675058*^9, 3.45792987275*^9},
 CellID->1007333637],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"-", "1.2800376594236917`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{
      RowBox[{"-", "0.9085622161438213`"}], "-", 
      RowBox[{"1.2544624559740705`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{
      RowBox[{"-", "0.9085622161438213`"}], "+", 
      RowBox[{"1.2544624559740705`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"0.19772589038864435`", "\[InvisibleSpace]", "-", 
      RowBox[{"1.3035239871964868`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"0.19772589038864435`", "\[InvisibleSpace]", "+", 
      RowBox[{"1.3035239871964868`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"1.3508551554670227`", "\[InvisibleSpace]", "-", 
      RowBox[{"0.4855799064132543`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"1.3508551554670227`", "\[InvisibleSpace]", "+", 
      RowBox[{"0.4855799064132543`", " ", "\[ImaginaryI]"}]}]}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.459152925625*^9, 3.461566842375*^9, 3.46979518196875*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Solve", "[", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"x", "^", "7"}], "-", 
      RowBox[{"2", 
       SuperscriptBox["x", "4"]}], "+", "11"}], "==", "0"}], ",", "x"}], 
   "]"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.427519142686263*^9, 3.427519160315199*^9}, 
   3.45792987928125*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"-", "1.2800376594236917`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{
      RowBox[{"-", "0.9085622161438213`"}], "-", 
      RowBox[{"1.2544624559740705`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{
      RowBox[{"-", "0.9085622161438213`"}], "+", 
      RowBox[{"1.2544624559740705`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"0.19772589038864435`", "\[InvisibleSpace]", "-", 
      RowBox[{"1.3035239871964868`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"0.19772589038864435`", "\[InvisibleSpace]", "+", 
      RowBox[{"1.3035239871964868`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"1.3508551554670227`", "\[InvisibleSpace]", "-", 
      RowBox[{"0.4855799064132543`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"1.3508551554670227`", "\[InvisibleSpace]", "+", 
      RowBox[{"0.4855799064132543`", " ", "\[ImaginaryI]"}]}]}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.45915292696875*^9, 3.461566842515625*^9, 3.469795182*^9}]
}, Open  ]],

Cell["\<\
Como podemos comprobar un polinomio con coeficientes reales, si tiene raices \
complejas, aparece siempre un valor y su conjugado como raices.\
\>", "Text",
 CellChangeTimes->{{3.427519166339572*^9, 3.427519216530878*^9}}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo 4\nObtener un valor aproximado de las soluciones de las siguientes \
ecuaciones:\na) ",
 Cell[BoxData[
  RowBox[{
   RowBox[{
    SuperscriptBox["x", "4"], "-", 
    RowBox[{"2", 
     SuperscriptBox["x", "2"]}]}], "=", 
   RowBox[{"1", "-", "x"}]}]]],
 " .\nb) ",
 Cell[BoxData[
  RowBox[{
   RowBox[{"1", "-", 
    SuperscriptBox["x", "2"]}], "=", 
   SuperscriptBox["x", "3"]}]]]
}], "Subsection"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"N", "[", 
  RowBox[{"Solve", "[", 
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "4"], "-", 
     RowBox[{"2", 
      SuperscriptBox["x", "2"]}]}], "==", 
    RowBox[{"1", "-", "x"}]}], "]"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"0.18277735123615813`", "\[InvisibleSpace]", "-", 
      RowBox[{"0.6333971164182438`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"0.18277735123615813`", "\[InvisibleSpace]", "+", 
      RowBox[{"0.6333971164182438`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"-", "1.710644095045033`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "1.3450893925727168`"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.4615668425625*^9, 3.46979518203125*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Solve", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"1", "-", 
      SuperscriptBox["x", "2"]}], "==", 
     SuperscriptBox["x", "3"]}], ",", "x"}], "]"}], "//", "N"}]], "Input"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "0.7548776662466917`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{
      RowBox[{"-", "0.8774388331233458`"}], "+", 
      RowBox[{"0.7448617666197448`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{
      RowBox[{"-", "0.8774388331233458`"}], "-", 
      RowBox[{"0.7448617666197448`", " ", "\[ImaginaryI]"}]}]}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.46156684259375*^9, 3.4697951820625*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"NSolve", "[", 
  RowBox[{
   RowBox[{
    SuperscriptBox["x", "4"], "-", 
    RowBox[{"2", 
     SuperscriptBox["x", "2"]}]}], "==", 
   RowBox[{"1", "-", "x"}]}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"-", "1.7106440950450328`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"0.1827773512361582`", "\[InvisibleSpace]", "-", 
      RowBox[{"0.6333971164182431`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"0.1827773512361582`", "\[InvisibleSpace]", "+", 
      RowBox[{"0.6333971164182431`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "1.3450893925727165`"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.461566842625*^9, 3.46979518209375*^9}]
}, Open  ]],

Cell[TextData[{
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " puede resolver ecuaciones que contienen m\[AAcute]s de una variable \
especific\[AAcute]ndole en qu\[EAcute] variable se quiere la \
resoluci\[OAcute]n. El resultado se puede interpretar como \"despejar la \
variable que se indica\" ."
}], "Text",
 CellChangeTimes->{{3.45915328353125*^9, 3.45915328728125*^9}},
 TextAlignment->Left,
 TextJustification->1],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "2"}], "+", 
     RowBox[{"2", "x", "*", "y"}], "-", 
     RowBox[{"y", "^", "2"}]}], "\[Equal]", "1"}], ",", "x"}], "]"}]], "Input",
 CellChangeTimes->{{3.459153299234375*^9, 3.45915331534375*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{
      RowBox[{"-", "y"}], "-", 
      SqrtBox[
       RowBox[{"1", "+", 
        RowBox[{"2", " ", 
         SuperscriptBox["y", "2"]}]}]]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{
      RowBox[{"-", "y"}], "+", 
      SqrtBox[
       RowBox[{"1", "+", 
        RowBox[{"2", " ", 
         SuperscriptBox["y", "2"]}]}]]}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.459153316421875*^9, 3.461566842671875*^9, 
  3.469795182125*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
Eliminando una inc\[OAcute]gnita en una ecuaci\[OAcute]n o un conjunto de \
ecuaciones polin\[OAcute]micas\
\>", "Section 1",
 CellChangeTimes->{{3.4275204146726933`*^9, 3.427520446417678*^9}}],

Cell[TextData[{
 "El comando ",
 StyleBox["Eliminate[ecuaciones, variables]",
  FontWeight->"Bold"],
 " nos permite eliminar o despejar  una o varias inc\[OAcute]gnitas entre \
varias ecuaciones polin\[OAcute]micas. Las ecuaciones deber\[AAcute]n ir \
entre llaves y separadas por comas o bien ligadas con el s\[IAcute]mbolo ",
 StyleBox["&&",
  FontWeight->"Bold"],
 ", que es el operador l\[OAcute]gico ",
 StyleBox["And",
  FontWeight->"Bold"]
}], "Text",
 CellChangeTimes->{{3.42751942053434*^9, 3.427519473993185*^9}, {
   3.4275195778419867`*^9, 3.427519582283784*^9}, {3.427519681210767*^9, 
   3.427519738460105*^9}, 3.4277779430396233`*^9}],

Cell[CellGroupData[{

Cell["\<\
Ejemplo 5
Eliminar z en las ecuaciones,
\t2x+3y+4z=1
\t9x+8y+7z=2\
\>", "Subsection",
 CellChangeTimes->{{3.427519495121357*^9, 3.4275195171945143`*^9}, {
  3.427519594378459*^9, 3.427519673742333*^9}, {3.427778038166032*^9, 
  3.4277780387110147`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Eliminate", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"2", "x"}], "+", 
       RowBox[{"3", "y"}], "+", 
       RowBox[{"4", "z"}]}], "\[Equal]", "1"}], ",", 
     RowBox[{
      RowBox[{
       RowBox[{"9", "x"}], "+", 
       RowBox[{"8", "y"}], "+", 
       RowBox[{"7", "z"}]}], "\[Equal]", "2"}]}], "}"}], ",", "z"}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.4275203373511477`*^9, 3.42752035342028*^9}},
 CellID->539162013],

Cell[BoxData[
 RowBox[{
  RowBox[{"1", "-", 
   RowBox[{"11", " ", "y"}]}], "\[Equal]", 
  RowBox[{"22", " ", "x"}]}]], "Output",
 CellChangeTimes->{3.46156684278125*^9, 3.469795182171875*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
Aproximaci\[OAcute]n num\[EAcute]rica de la soluci\[OAcute]n de una ecuaci\
\[OAcute]n\
\>", "Section 1"],

Cell[TextData[{
 "Cuando es imposible resolver anal\[IAcute]ticamente o de forma exacta una \
ecuaci\[OAcute]n, ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " dispone de varios comando que permiten obtener una soluci\[OAcute]n \
aproximada. Estos comandos son FindRoot, NRoots y NSolve. El comando NRoots \
sirve ecuaciones polin\[OAcute]micas. El comando FindRoot necesita una \
aproximaci\[OAcute]n inicial a partir de la cual realiza el c\[AAcute]lculo \
de la raiz. Para obtener esta aproximaci\[OAcute]n inicial lo mejor, siempre \
que sea posible es realizar las gr\[AAcute]ficas correspondientes."
}], "Text",
 CellChangeTimes->{{3.427520496835723*^9, 3.427520497846869*^9}, 
   3.45793148690625*^9, {3.459153173125*^9, 3.45915324434375*^9}},
 TextAlignment->Left,
 TextJustification->1],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo 6\nObtener las soluciones aproximadas de la ecuaci\[OAcute]n:\n",
 Cell[BoxData[
  RowBox[{
   RowBox[{
    RowBox[{"x", "^", "7"}], "-", 
    RowBox[{"2", 
     SuperscriptBox["x", "4"]}], "+", 
    RowBox[{"6", 
     SuperscriptBox["x", "2"]}], "-", "2"}], "=", "0"}]],
  CellChangeTimes->{{3.457930757875*^9, 3.457930819546875*^9}}]
}], "Subsection",
 CellChangeTimes->{
  3.427520516564314*^9, {3.427778043658533*^9, 3.42777804414909*^9}, {
   3.45793073315625*^9, 3.45793074875*^9}, {3.4579308281875*^9, 
   3.457930833765625*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"NRoots", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "7"}], "-", 
     RowBox[{"2", 
      SuperscriptBox["x", "4"]}], "+", 
     RowBox[{"6", 
      SuperscriptBox["x", "2"]}], "-", "2"}], "==", "0"}], ",", "x"}], 
  "]"}]], "Input",
 CellChangeTimes->{3.4579306985625*^9, 3.45793073796875*^9, 
  3.457930831171875*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"x", "\[Equal]", 
   RowBox[{"-", "1.1337562278058309`"}]}], "||", 
  RowBox[{"x", "\[Equal]", 
   RowBox[{"-", "0.6247424245153483`"}]}], "||", 
  RowBox[{"x", "\[Equal]", 
   RowBox[{
    RowBox[{"-", "0.5819976870410729`"}], "-", 
    RowBox[{"1.5010745352317583`", " ", "\[ImaginaryI]"}]}]}], "||", 
  RowBox[{"x", "\[Equal]", 
   RowBox[{
    RowBox[{"-", "0.5819976870410729`"}], "+", 
    RowBox[{"1.5010745352317583`", " ", "\[ImaginaryI]"}]}]}], "||", 
  RowBox[{"x", "\[Equal]", "0.6121950386886468`"}], "||", 
  RowBox[{"x", "\[Equal]", 
   RowBox[{"1.155149493857339`", "\[InvisibleSpace]", "-", 
    RowBox[{"0.667166713644494`", " ", "\[ImaginaryI]"}]}]}], "||", 
  RowBox[{"x", "\[Equal]", 
   RowBox[{"1.155149493857339`", "\[InvisibleSpace]", "+", 
    RowBox[{"0.667166713644494`", " ", "\[ImaginaryI]"}]}]}]}]], "Output",
 CellChangeTimes->{3.461566842828125*^9, 3.469795182203125*^9}]
}, Open  ]],

Cell[TextData[{
 "El s\[IAcute]mbolo || de la respuesta representa al operador l\[OAcute]gico \
 \"",
 StyleBox["OR",
  FontWeight->"Bold"],
 "\""
}], "Text",
 CellChangeTimes->{{3.4275205297720957`*^9, 3.427520560155941*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"?", "||"}]], "Input"],

Cell[BoxData[
 RowBox[{
  StyleBox["\<\"\!\(\*RowBox[{SubscriptBox[StyleBox[\\\"e\\\", \\\"TI\\\"], \
StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\"||\\\", \
SubscriptBox[StyleBox[\\\"e\\\", \\\"TI\\\"], StyleBox[\\\"2\\\", \
\\\"TR\\\"]], \\\"||\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\"TR\\\"]}]\) is \
the logical OR function. It evaluates its arguments in order, giving True \
immediately if any of them are True, and False if they are all False. \"\>", 
   "MSG"], "\[NonBreakingSpace]", 
  ButtonBox[
   StyleBox["\[RightSkeleton]", "SR"],
   Active->True,
   BaseStyle->"Link",
   ButtonData->"paclet:ref/Or"]}]], "Print", "PrintUsage",
 CellChangeTimes->{3.46979518246875*^9},
 CellTags->"Info3469798782-9119275"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"NSolve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "7"}], "-", 
     RowBox[{"2", 
      SuperscriptBox["x", "4"]}], "+", 
     RowBox[{"6", 
      SuperscriptBox["x", "2"]}], "-", "2"}], "==", "0"}], ",", "x"}], 
  "]"}]], "Input",
 CellChangeTimes->{3.457930746890625*^9, 3.45793084459375*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"-", "1.1337562278058309`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"-", "0.6247424245153483`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{
      RowBox[{"-", "0.5819976870410729`"}], "-", 
      RowBox[{"1.5010745352317583`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{
      RowBox[{"-", "0.5819976870410729`"}], "+", 
      RowBox[{"1.5010745352317583`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "0.6121950386886468`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"1.155149493857339`", "\[InvisibleSpace]", "-", 
      RowBox[{"0.667166713644494`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"1.155149493857339`", "\[InvisibleSpace]", "+", 
      RowBox[{"0.667166713644494`", " ", "\[ImaginaryI]"}]}]}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.461566843625*^9, 3.4697951825625*^9}]
}, Open  ]],

Cell[TextData[{
 "El comando ",
 StyleBox["FindRoot[f, {x,",
  FontWeight->"Bold"],
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "0"], TraditionalForm]],
  FontWeight->"Bold"],
 StyleBox["}] ",
  FontWeight->"Bold"],
 "obtiene la soluci\[OAcute]n num\[EAcute]rica de una ecuaci\[OAcute]n o un \
sistema. Este comando implementa el m\[EAcute]todo num\[EAcute]rico de Newton \
- Raphson y necesita una aproximaci\[OAcute]n inicial, que ir\[AAcute] entre \
llaves con la inc\[OAcute]gnita separada por una coma. Para tener idea del \
valor de la aproximaci\[OAcute]n inicial conviene hacer una representaci\
\[OAcute]n gr\[AAcute]fica.\nVamos a obtener mediante este comando las raices \
reales de la ecuaci\[OAcute]n anterior. Para ello, en primer lugar, \
representamos gr\[AAcute]ficamente la funci\[OAcute]n polin\[OAcute]mica."
}], "Text",
 CellChangeTimes->{{3.4275205911892776`*^9, 3.427520593457205*^9}, {
  3.4275206615213537`*^9, 3.4275208105454903`*^9}, {3.427520850282934*^9, 
  3.427521025224519*^9}},
 TextAlignment->Left,
 TextJustification->1.],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "7"}], "-", 
     RowBox[{"2", 
      SuperscriptBox["x", "4"]}], "+", 
     RowBox[{"6", 
      SuperscriptBox["x", "2"]}], "-", "2"}], "==", "0"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.457930757875*^9, 3.457930819546875*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwVl3c41e8bx4XIFmVnhZCVlZGejxIqm6SSSlKpkIyKMpJEhC9FIdGQZESR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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{-2, 2}, {-22.40417015700642, 26.663160847379853`}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.46156684371875*^9, 3.469795182609375*^9}]
}, Open  ]],

Cell["\<\
En esta gr\[AAcute]fica se ve que la funci\[OAcute]n tiene tres raices \
reales. Tres buenas aproximaciones para estas tres raices son : -2.5, -1 y 2.\
\>", "Text",
 CellChangeTimes->{{3.427521053818596*^9, 3.4275210978990393`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindRoot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "7"}], "-", 
     RowBox[{"2", 
      SuperscriptBox["x", "4"]}], "+", 
     RowBox[{"6", 
      SuperscriptBox["x", "2"]}], "-", "2"}], "==", "0"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "1"}]}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.4579308600625*^9, 3.457930865140625*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"x", "\[Rule]", 
   RowBox[{"-", "1.1337562278058309`"}]}], "}"}]], "Output",
 CellChangeTimes->{3.461566844703125*^9, 3.469795182671875*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindRoot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "7"}], "-", 
     RowBox[{"2", 
      SuperscriptBox["x", "4"]}], "+", 
     RowBox[{"6", 
      SuperscriptBox["x", "2"]}], "-", "2"}], "==", "0"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{
      RowBox[{"-", "1"}], "/", "2"}]}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.457930876890625*^9, 3.457930882546875*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"x", "\[Rule]", 
   RowBox[{"-", "0.6247424245153483`"}]}], "}"}]], "Output",
 CellChangeTimes->{3.461566844765625*^9, 3.469795182703125*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindRoot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "7"}], "-", 
     RowBox[{"2", 
      SuperscriptBox["x", "4"]}], "+", 
     RowBox[{"6", 
      SuperscriptBox["x", "2"]}], "-", "2"}], "==", "0"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.457930889328125*^9, 3.4579308955625*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"x", "\[Rule]", "0.6121950386886468`"}], "}"}]], "Output",
 CellChangeTimes->{3.461566844796875*^9, 3.469795182734375*^9}]
}, Open  ]],

Cell["\<\
Tambien podemos utilizar el comando para obtener una raiz compleja aunque en \
este caso puede resultar m\[AAcute]s dif\[IAcute]cil dar una buena aproximaci\
\[OAcute]n inicial.\
\>", "Text",
 CellChangeTimes->{{3.42752118449511*^9, 3.427521235393392*^9}, {
  3.427521295085634*^9, 3.427521300775399*^9}, {3.427521398434411*^9, 
  3.427521405231832*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindRoot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "7"}], "-", 
     RowBox[{"2", 
      SuperscriptBox["x", "4"]}], "+", 
     RowBox[{"6", 
      SuperscriptBox["x", "2"]}], "-", "2"}], "==", "0"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{
      RowBox[{"-", "0.5"}], "-", 
      RowBox[{"1.5", "I"}]}]}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.4579309128125*^9, 3.457930924203125*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"x", "\[Rule]", 
   RowBox[{
    RowBox[{"-", "0.5819976870410729`"}], "-", 
    RowBox[{"1.5010745352317583`", " ", "\[ImaginaryI]"}]}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.461566845171875*^9, 3.46979518284375*^9}]
}, Open  ]],

Cell[TextData[{
 "La soluci\[OAcute]n que nos da este comando es del mismo tipo que la que \
proporciona Solve, es decir, no es un n\[UAcute]mero, sino que ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " nos dice qu\[EAcute] valor hay que asignar a la inc\[OAcute]gnita para \
tener la soluci\[OAcute]n. Para sacar el n\[UAcute]mero hay que utilizar el \
operador reemplazamiento."
}], "Text",
 CellChangeTimes->{{3.42752135026117*^9, 3.427521378930348*^9}, {
  3.4275214221551657`*^9, 3.427521507567422*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
Ejemplo 7
Aproximar las soluciones positivas de la ecuaci\[OAcute]n:
cos(x)-x = 0\
\>", "Subsection",
 CellChangeTimes->{{3.427521316509486*^9, 3.427521316910631*^9}, {
  3.427778070930575*^9, 3.427778071729713*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "f", "]"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x_", "]"}], "=", 
   RowBox[{
    RowBox[{"Cos", "[", "x", "]"}], "-", "x"}]}], ";"}], "\n", 
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"f", "[", "x", "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]}], "Input"],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwtlH8803kcx/08ui5G57oR+dnJj7hOnVDvrnWmDT2wWiqlMtVSJ+lc5R6s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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 1}, {-0.45969765655081984`, 0.9999999795918365}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.461566845203125*^9, 3.469795182890625*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindRoot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"f", "[", "x", "]"}], "==", "0"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0.7"}], "}"}]}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"x", "\[Rule]", "0.7390851332151608`"}], "}"}]], "Output",
 CellChangeTimes->{3.46156684521875*^9, 3.46979518290625*^9}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo 8\nAproximar los puntos de intersecci\[OAcute]n de las curvas: \n\
f(x) = log(6x) y g(x)=sen(",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     RowBox[{"5", 
      SuperscriptBox["x", 
       RowBox[{"3", "/", "2"}]]}], ")"}], "+", 
    RowBox[{"5", "/", "4."}]}], TraditionalForm]]]
}], "Subsection",
 CellChangeTimes->{{3.4277781458420353`*^9, 3.427778146726212*^9}, {
  3.457931123*^9, 3.457931148296875*^9}}],

Cell["\<\
En primer lugar hacemos la representaci\[OAcute]n gr\[AAcute]fica de ambas \
funciones. Podemos probar con distintos intervalo de x para la representaci\
\[OAcute]n gr\[AAcute]fica para localizar  claramente las raices.\
\>", "Text",
 CellChangeTimes->{{3.459153386484375*^9, 3.459153393328125*^9}},
 TextAlignment->Left,
 TextJustification->1.],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", 
  RowBox[{"f", ",", "g"}], "]"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x_", "]"}], "=", 
   RowBox[{"Log", "[", 
    RowBox[{"6", "x"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"g", "[", "x_", "]"}], "=", 
   RowBox[{
    RowBox[{"Sin", "[", 
     RowBox[{"5", 
      SuperscriptBox["x", 
       RowBox[{"3", "/", "2"}]]}], "]"}], "+", 
    FractionBox["5", "4"]}]}], ";"}], "\n", 
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"f", "[", "x", "]"}], ",", 
     RowBox[{"g", "[", "x", "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "3.5"}], "}"}], ",", 
   RowBox[{"PlotStyle", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"RGBColor", "[", 
       RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", 
      RowBox[{"RGBColor", "[", 
       RowBox[{"0", ",", "0", ",", "1"}], "]"}]}], "}"}]}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.457931046171875*^9, 3.457931110640625*^9}, 
   3.457931143546875*^9, {3.457931185546875*^9, 3.45793118946875*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {RGBColor[1, 0, 0], LineBox[CompressedData["
1:eJwVlHs4lHkfxmfG4OEpvSwllVNWlKbTVtj0/UUp2xjHFFKpkAZR7VhskhRK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     "]]}, 
   {RGBColor[0, 0, 1], LineBox[CompressedData["
1:eJwUmnk8lF8bxucZY4ylCCFSkbUQEpLcp6gkCamkRGTLEpItJBRRIYWi8muR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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 3.5}, {-2.285790394830536, 3.0445224173152594`}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.461566845296875*^9, 3.46979518296875*^9}]
}, Open  ]],

Cell["\<\
Para obtener una buena aproximaci\[OAcute]n se marca el gr\[AAcute]fico y \
despu\[EAcute]s pulsando la tecla Ctrl+d aparece una paleta en la que \
pinchando en la cruz se pudeen saber las  coordenadas de cualquier punto del \
gr\[AAcute]fico.\
\>", "Text",
 CellChangeTimes->{{3.45793124721875*^9, 3.4579312954375*^9}, 
   3.45915340090625*^9},
 TextAlignment->Left,
 TextJustification->1],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"s4", "=", 
  RowBox[{"FindRoot", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"f", "[", "x", "]"}], "==", 
     RowBox[{"g", "[", "x", "]"}]}], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", "0.7"}], "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.457931312921875*^9, 3.45793131340625*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"x", "\[Rule]", "0.7035073986014247`"}], "}"}]], "Output",
 CellChangeTimes->{3.461566845328125*^9, 3.469795183*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"x1", "=", 
  RowBox[{"x", "/.", "s4"}]}]], "Input"],

Cell[BoxData["0.7035073986014247`"], "Output",
 CellChangeTimes->{3.461566845359375*^9, 3.469795183015625*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"N", "[", 
  RowBox[{"f", "[", "x1", "]"}], "]"}]], "Input"],

Cell[BoxData["1.4400825835914348`"], "Output",
 CellChangeTimes->{3.461566845390625*^9, 3.469795183046875*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"s5", "=", 
  RowBox[{"FindRoot", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"f", "[", "x", "]"}], "==", 
     RowBox[{"g", "[", "x", "]"}]}], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", "1.27"}], "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.4579313333125*^9, 3.457931333984375*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"x", "\[Rule]", "1.273197270157049`"}], "}"}]], "Output",
 CellChangeTimes->{3.46156684540625*^9, 3.469795183078125*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"x2", "=", 
  RowBox[{"x", "/.", "s5"}]}]], "Input"],

Cell[BoxData["1.273197270157049`"], "Output",
 CellChangeTimes->{3.4615668454375*^9, 3.469795183109375*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"N", "[", 
  RowBox[{"f", "[", "x2", "]"}], "]"}]], "Input"],

Cell[BoxData["2.0332907415713253`"], "Output",
 CellChangeTimes->{3.461566845453125*^9, 3.469795183140625*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"s6", "=", 
  RowBox[{"FindRoot", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"f", "[", "x", "]"}], "==", 
     RowBox[{"g", "[", "x", "]"}]}], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", "1.4"}], "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.4579313565*^9, 3.457931372046875*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"x", "\[Rule]", "1.40674899220211`"}], "}"}]], "Output",
 CellChangeTimes->{3.461566845484375*^9, 3.46979518315625*^9}]
}, Open  ]],

Cell["\<\
Podemos resolver tambi\[EAcute]n un sistema de ecuaciones no lineales. Como \
en el caso de una \[UAcute]nica ecuaci\[OAcute]n ser\[AAcute] necesario \
indicar junto con cada inc\[OAcute]gnita la aproximaci\[OAcute]n inicial.\
\>", "Text",
 CellChangeTimes->{{3.427521617583301*^9, 3.427521664896291*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindRoot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"Sin", "[", 
      RowBox[{"x", "+", "y"}], "]"}], ",", 
     RowBox[{"Cos", "[", 
      RowBox[{"x", "-", "y"}], "]"}], ",", 
     RowBox[{
      RowBox[{"x", "^", "2"}], "+", 
      RowBox[{"y", "^", "2"}], "-", "z"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"x", ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", "0"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", "0"}], "}"}]}], "}"}]}], "]"}]], "Input",
 CellID->85154930],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"x", "\[Rule]", "0.7853981633974483`"}], ",", 
   RowBox[{"y", "\[Rule]", 
    RowBox[{"-", "0.7853981633974483`"}]}], ",", 
   RowBox[{"z", "\[Rule]", "1.2337005501361697`"}]}], "}"}]], "Output",
 CellChangeTimes->{3.461566845515625*^9, 3.4697951831875*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell["\<\
Resoluci\[OAcute]n de ecuaciones e inecuaciones\
\>", "Section 1",
 CellChangeTimes->{{3.427630357335984*^9, 3.427630369045012*^9}}],

Cell[CellGroupData[{

Cell["El comando FindInstance", "Section",
 CellChangeTimes->{{3.4276969860862103`*^9, 3.4276969916874723`*^9}}],

Cell[TextData[{
 "Mathematica dispone del comando ",
 StyleBox["FindInstance ",
  FontWeight->"Bold"],
 "que da una soluci\[OAcute]n particular de forma similar al comando ",
 StyleBox["Solve",
  FontWeight->"Bold"],
 ".\nLa sintaxis m\[AAcute]s sencilla es:\n",
 StyleBox["\tFindInstance[expr, variables]\n",
  FontWeight->"Bold"],
 "La soluci\[OAcute]n obtenida en las variables hace verdadera a expr. \n\
Expr. puede contener ecuaciones, inecuaciones y especificaciones de dominio.\n\
Si el argumento es un valor exacto entonces el resultado tambi\[EAcute]n lo \
ser\[AAcute]."
}], "Text",
 CellChangeTimes->{{3.42763037922237*^9, 3.427630465890265*^9}, {
   3.427630502827949*^9, 3.4276307594761353`*^9}, {3.4276315123067083`*^9, 
   3.427631524543754*^9}, {3.427632012845222*^9, 3.4276320172946997`*^9}, 
   3.45915343459375*^9}],

Cell[TextData[{
 "Por ejemplo, una soluci\[OAcute]n del conjunto de soluciones que verifican \
el sistema :\n\t",
 Cell[BoxData[
  FormBox[
   TagBox[
    StyleBox[
     RowBox[{"{", 
      StyleBox[GridBox[{
         {
          RowBox[{
           RowBox[{
            SuperscriptBox["x", "2"], "+", 
            SuperscriptBox["y", "2"], "+", 
            SuperscriptBox["z", "2"]}], "=", 
           RowBox[{"-", "1"}]}]},
         {
          RowBox[{
           SuperscriptBox["z", "2"], "=", 
           RowBox[{
            RowBox[{"2", "x"}], "-", 
            RowBox[{"5", "y"}]}]}]}
        }],
       ShowAutoStyles->True]}],
     ShowAutoStyles->False],
    #& ], TraditionalForm]]],
 "\nse puede obener,"
}], "Text",
 CellChangeTimes->{{3.427648945897633*^9, 3.4276490474420967`*^9}, {
  3.427649084072817*^9, 3.427649105434977*^9}, {3.4276495612778397`*^9, 
  3.427649572283721*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindInstance", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"x", "^", "2"}], "+", 
      RowBox[{"y", "^", "2"}], "+", 
      RowBox[{"z", "^", "2"}]}], "\[Equal]", 
     RowBox[{"-", "1"}]}], "&&", 
    RowBox[{
     RowBox[{"z", "^", "2"}], "\[Equal]", 
     RowBox[{
      RowBox[{"2", "x"}], "-", 
      RowBox[{"5", " ", "y"}]}]}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.427630892584937*^9, 3.427630895397917*^9}},
 CellID->47420189],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"x", "\[Rule]", "0"}], ",", 
    RowBox[{"y", "\[Rule]", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      RowBox[{"(", 
       RowBox[{"5", "-", 
        SqrtBox["21"]}], ")"}]}]}], ",", 
    RowBox[{"z", "\[Rule]", 
     RowBox[{
      RowBox[{"-", "\[ImaginaryI]"}], " ", 
      SqrtBox[
       RowBox[{
        FractionBox["5", "2"], " ", 
        RowBox[{"(", 
         RowBox[{"5", "-", 
          SqrtBox["21"]}], ")"}]}]]}]}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.459153448125*^9, 3.461566846546875*^9, 
  3.469795183390625*^9}]
}, Open  ]],

Cell[TextData[{
 "Para obtener una soluci\[OAcute]n real del sistema :\n\t",
 Cell[BoxData[
  FormBox[
   TagBox[
    StyleBox[
     RowBox[{"{", 
      StyleBox[GridBox[{
         {
          RowBox[{
           RowBox[{
            SuperscriptBox["x", "2"], "+", 
            SuperscriptBox["y", "2"], "+", 
            SuperscriptBox["z", "2"]}], "\[LessEqual]", "1"}]},
         {
          RowBox[{
           RowBox[{"9", 
            SuperscriptBox["z", "3"]}], "=", 
           RowBox[{
            RowBox[{"2", "x"}], "-", 
            RowBox[{"5", "y"}], "-", "7"}]}]}
        }],
       ShowAutoStyles->True]}],
     ShowAutoStyles->False],
    #& ], TraditionalForm]]],
 "\na\[NTilde]adimos la opci\[OAcute]n Reals."
}], "Text",
 CellChangeTimes->{{3.427649589073806*^9, 3.427649711579362*^9}, {
  3.459153686859375*^9, 3.459153701296875*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindInstance", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"x", "^", "2"}], "+", 
      RowBox[{"y", "^", "2"}], "+", 
      RowBox[{"z", "^", "2"}]}], "\[LessEqual]", "1"}], "&&", 
    RowBox[{
     RowBox[{"9", 
      RowBox[{"z", "^", "3"}]}], "\[Equal]", 
     RowBox[{
      RowBox[{"2", "x"}], "-", 
      RowBox[{"5", " ", "y"}], "-", "7"}]}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y", ",", "z"}], "}"}], ",", "Reals"}], "]"}]], "Input",
 CellChangeTimes->{{3.427631036493123*^9, 3.427631058437057*^9}},
 CellID->60662809],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"x", "\[Rule]", 
     FractionBox["45", "128"]}], ",", 
    RowBox[{"y", "\[Rule]", 
     RowBox[{"-", 
      FractionBox["1", "2"]}]}], ",", 
    RowBox[{"z", "\[Rule]", 
     RowBox[{"-", 
      FractionBox["3", "4"]}]}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.4591534546875*^9, 3.461566847265625*^9, 
  3.46979518346875*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo 9\nEncontrar dos soluciones de la inecuaci\[OAcute]n:\n\t",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "2"], "+", 
     SuperscriptBox["y", "2"]}], "\[LessEqual]", "1"}], TraditionalForm]]],
 " con x<1\nRepresentarlas gr\[AAcute]ficamente para comprobar que  verifican \
la incecuaci\[OAcute]n"
}], "Subsection",
 CellChangeTimes->{{3.4276510001136723`*^9, 3.427651002284696*^9}, {
  3.427651085390567*^9, 3.4276511705851307`*^9}, {3.427696139274692*^9, 
  3.42769615353659*^9}, {3.427696214347652*^9, 3.427696254694931*^9}, {
  3.427778232378475*^9, 3.427778234945902*^9}}],

Cell["\<\
En este ejemplo se representan gr\[AAcute]ficamente los puntos cuyas \
coordenadas son las dos soluciones de la inecuaci\[OAcute]n dadas por el \
comando FindInstance, utilizando una combinaci\[OAcute]n de los comandos \
Graphics y Point.\
\>", "Text",
 CellChangeTimes->{{3.459153480203125*^9, 3.45915357390625*^9}, {
  3.45915362659375*^9, 3.4591536413125*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"sol3", "=", 
  RowBox[{"FindInstance", "[", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"x", "^", "2"}], "+", 
       RowBox[{"y", "^", "2"}]}], "\[LessEqual]", "1"}], "&&", 
     RowBox[{"x", "<", "1"}]}], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y"}], "}"}], ",", "2"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.427631108120019*^9, 3.4276311974492807`*^9}, {
  3.427651190763026*^9, 3.427651194067403*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"x", "\[Rule]", 
      RowBox[{"-", 
       FractionBox["92", "101"]}]}], ",", 
     RowBox[{"y", "\[Rule]", 
      FractionBox["12", "41"]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"x", "\[Rule]", 
      RowBox[{"-", "1"}]}], ",", 
     RowBox[{"y", "\[Rule]", "0"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.459153644046875*^9, 3.461566847609375*^9, 
  3.4697951835*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{"Clear", "[", "ptos", "]"}]], "Input",
 CellChangeTimes->{{3.427651198809423*^9, 3.427651204867831*^9}, {
  3.427651238537438*^9, 3.427651239646913*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ptos", "=", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", ",", "y"}], "}"}], "/.", "sol3"}]}]], "Input",
 CellChangeTimes->{{3.427651242177884*^9, 3.4276512681578827`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", 
      FractionBox["92", "101"]}], ",", 
     FractionBox["12", "41"]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.459153646640625*^9, 3.461566847671875*^9, 
  3.46979518353125*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"g4", "=", 
   RowBox[{"RegionPlot", "[", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"x", "^", "2"}], "+", 
       RowBox[{"y", "^", "2"}]}], "\[LessEqual]", "1"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", 
     RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.427651415151704*^9, 3.4276514204688187`*^9}, {
   3.4276514632097263`*^9, 3.427651623836246*^9}, 3.427651683029986*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"g5", "=", 
   RowBox[{"Graphics", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"PointSize", "[", "Large", "]"}], ",", 
      RowBox[{"Point", "[", "ptos", "]"}]}], "}"}], "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.427651628497839*^9, 3.427651674976355*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{"g4", ",", "g5"}], "]"}]], "Input",
 CellChangeTimes->{{3.4276516909978523`*^9, 3.4276516995772457`*^9}}],

Cell[BoxData[
 GraphicsBox[{GraphicsComplexBox[CompressedData["
1:eJxlmHtw1cUVx1NqrQ+iyETUAEHlFeRhSnMjUOBIY3lV2xARMrYNImMLxIqC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    "], {{
      {RGBColor[0.798413061722744, 0.824719615472648, 0.968322270542458], 
       EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
1:eJxNmXeclsURx3dWQYo06f0OpIkI0ttRjir9EFQIEAKCIEoRFUWkKGJD7DUI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          "]], PolygonBox[CompressedData["
1:eJwtlXmwj1UYx89zrutW3CVUWjTUTMuEaVGa0oymMU3TMrJndynaSLSgJpom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          "]]}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], Opacity[0.4], LineBox[CompressedData["
1:eJwl1FWYVQUUgNE7SEkLStcoCNIN0iktJR3SDUNLK50GCEipdHdJI93d3Skh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       "]]}}], 
   {PointSize[Large], 
    PointBox[NCache[{{Rational[-92, 101], Rational[12, 41]}, {-1, 
       0}}, {{-0.9108910891089109, 0.2926829268292683}, {-1, 0}}]]}},
  Frame->True,
  Method->{"TransparentPolygonMesh" -> True, "AxesInFront" -> True},
  PlotRange->{{-1, 1}, {-2, 2}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.459153653703125*^9, 3.46156684778125*^9, 
  3.469795183625*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["El comando Reduce", "Section",
 CellChangeTimes->{{3.42769701148676*^9, 3.4276970145996113`*^9}}],

Cell[TextData[{
 "El comando Reduce simplifica la expresi\[OAcute]n resolviendo ecuaciones e \
inecuaciones. Su sintaxis es :\n",
 StyleBox["\tReduce[expr, variables]\n",
  FontWeight->"Bold"],
 "La salida del comando describe matem\[AAcute]ticamente el mismo conjunto \
que expr. Se puede especificar tambi\[EAcute]n el dominio al que debe \
pertener la soluci\[OAcute]n. Los m\[AAcute]s habituales son Integer, Real o \
Complex. \n\nEn las salidas debemos interpretar el s\[IAcute]mbolo && como el \
And l\[OAcute]gico, y el s\[IAcute]mbolo ",
 "|| como el Or l\[OAcute]gico."
}], "Text",
 CellChangeTimes->{{3.427632020951356*^9, 3.427632110337541*^9}, {
  3.427632155921681*^9, 3.427632294898506*^9}, {3.459154053046875*^9, 
  3.459154115328125*^9}},
 TextAlignment->Left,
 TextJustification->1.],

Cell[TextData[{
 "El conjunto de valores de x e y que verifican ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "2"], "+", 
     SuperscriptBox["y", "2"]}], "<", "1"}], TraditionalForm]]]
}], "Text",
 CellChangeTimes->{{3.4276518583111677`*^9, 3.4276519078418713`*^9}, {
  3.427651985223126*^9, 3.4276519876316357`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Reduce", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "2"}], "+", 
     RowBox[{"y", "^", "2"}]}], "<", "1"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y"}], "}"}]}], "]"}]], "Input",
 CellID->15483236],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"-", "1"}], "<", "x", "<", "1"}], "&&", 
  RowBox[{
   RowBox[{"-", 
    SqrtBox[
     RowBox[{"1", "-", 
      SuperscriptBox["x", "2"]}]]}], "<", "y", "<", 
   SqrtBox[
    RowBox[{"1", "-", 
     SuperscriptBox["x", "2"]}]]}]}]], "Output",
 CellChangeTimes->{3.461566847796875*^9, 3.469795183640625*^9}]
}, Open  ]],

Cell[TextData[{
 "El conjunto de valores de x e y que verifican ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "2"], "-", 
     RowBox[{"7", 
      SuperscriptBox["y", "2"]}]}], "=", "1"}], TraditionalForm]]],
 " con x>0 e y>0"
}], "Text",
 CellChangeTimes->{{3.427652027849949*^9, 3.427652037314539*^9}, {
  3.427652120357567*^9, 3.427652195892223*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Reduce", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"x", "^", "2"}], "-", 
      RowBox[{"7", 
       RowBox[{"y", "^", "2"}]}]}], "\[Equal]", "1"}], "&&", 
    RowBox[{"x", ">", "0"}], "&&", 
    RowBox[{"y", ">", "0"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y"}], "}"}], ",", "Reals"}], "]"}]], "Input",
 CellChangeTimes->{{3.427652001732354*^9, 3.427652015865838*^9}},
 CellID->118871955],

Cell[BoxData[
 RowBox[{
  RowBox[{"x", ">", "1"}], "&&", 
  RowBox[{"y", "\[Equal]", 
   FractionBox[
    SqrtBox[
     RowBox[{
      RowBox[{"-", "1"}], "+", 
      SuperscriptBox["x", "2"]}]], 
    SqrtBox["7"]]}]}]], "Output",
 CellChangeTimes->{3.461566847859375*^9, 3.469795183734375*^9}]
}, Open  ]],

Cell[TextData[{
 "El conjunto de valores {x, y, z } reales que verifican ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "2"], "-", "yz"}], " ", "=", " ", "1"}], 
   TraditionalForm]]]
}], "Text",
 CellChangeTimes->{{3.427652704410445*^9, 3.427652771746973*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Reduce", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "2"}], "-", 
     RowBox[{"y", " ", "z"}]}], "\[Equal]", "1"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y", ",", "z"}], "}"}], ",", "Reals"}], "]"}]], "Input",
 CellID->758827168],

Cell[BoxData[
 RowBox[{
  RowBox[{"(", 
   RowBox[{
    RowBox[{"x", "\[Equal]", 
     RowBox[{"-", "1"}]}], "&&", 
    RowBox[{"y", "\[Equal]", "0"}]}], ")"}], "||", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{"x", "\[Equal]", "1"}], "&&", 
    RowBox[{"y", "\[Equal]", "0"}]}], ")"}], "||", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"y", "<", "0"}], "||", 
      RowBox[{"y", ">", "0"}]}], ")"}], "&&", 
    RowBox[{"z", "\[Equal]", 
     RowBox[{"-", 
      FractionBox[
       RowBox[{"1", "-", 
        SuperscriptBox["x", "2"]}], "y"]}]}]}], ")"}]}]], "Output",
 CellChangeTimes->{3.461566848125*^9, 3.469795183796875*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo 10\nDescribir matem\[AAcute]ticamente el conjunto de valores reales \
de {x, y, z} que  verifican  ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["x", "2"], TraditionalForm]]],
 "-2y + ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["z", "2"], TraditionalForm]]],
 "\[LessEqual] 1. "
}], "Subsection",
 CellChangeTimes->{{3.427652885181555*^9, 3.427652933103829*^9}, {
  3.4277782844537563`*^9, 3.4277782874792423`*^9}, {3.459153808703125*^9, 
  3.459153877515625*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Reduce", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "2"}], "-", 
     RowBox[{"2", "y"}], " ", "+", 
     RowBox[{"z", "^", "2"}]}], "\[LessEqual]", "1"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y", ",", "z"}], "}"}], ",", "Reals"}], "]"}]], "Input",
 CellID->223254230],

Cell[BoxData[
 RowBox[{
  RowBox[{"(", 
   RowBox[{
    RowBox[{"y", "\[Equal]", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"-", "1"}], "+", 
        SuperscriptBox["x", "2"]}], ")"}]}]}], "&&", 
    RowBox[{"z", "\[Equal]", "0"}]}], ")"}], "||", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{"y", ">", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"-", "1"}], "+", 
        SuperscriptBox["x", "2"]}], ")"}]}]}], "&&", 
    RowBox[{
     RowBox[{"-", 
      SqrtBox[
       RowBox[{"1", "-", 
        SuperscriptBox["x", "2"], "+", 
        RowBox[{"2", " ", "y"}]}]]}], "\[LessEqual]", "z", "\[LessEqual]", 
     SqrtBox[
      RowBox[{"1", "-", 
       SuperscriptBox["x", "2"], "+", 
       RowBox[{"2", " ", "y"}]}]]}]}], ")"}]}]], "Output",
 CellChangeTimes->{3.45915388096875*^9, 3.46156684815625*^9, 
  3.46979518384375*^9}]
}, Open  ]],

Cell[TextData[{
 "La interpretaci\[OAcute]n de este resultado es la siguiente :\n1\.ba) z = 0 \
e y = ",
 Cell[BoxData[
  RowBox[{
   FractionBox["1", "2"], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"-", "1"}], "+", 
     SuperscriptBox["x", "2"]}], ")"}]}]],
  CellChangeTimes->{3.45915388096875*^9}],
 " con cualquier valor de x.\n\to\n2\.ba) y > ",
 Cell[BoxData[
  RowBox[{
   FractionBox["1", "2"], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"-", "1"}], "+", 
     SuperscriptBox["x", "2"]}], ")"}]}]],
  CellChangeTimes->{3.45915388096875*^9}],
 "y ",
 Cell[BoxData[
  RowBox[{
   RowBox[{
    RowBox[{"-", 
     SqrtBox[
      RowBox[{"1", "-", 
       SuperscriptBox["x", "2"], "+", 
       RowBox[{"2", " ", "y"}]}]]}], "\[LessEqual]", "z", "\[LessEqual]", 
    SqrtBox[
     RowBox[{"1", "-", 
      SuperscriptBox["x", "2"], "+", 
      RowBox[{"2", " ", "y"}]}]]}], ")"}]],
  CellChangeTimes->{3.45915388096875*^9}],
 " con cualquier valor de x."
}], "Text",
 CellChangeTimes->{{3.459153896046875*^9, 3.459154018296875*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo 11\nHallar los valores reales que verifican:\n\t",
 Cell[BoxData[
  FormBox[
   TagBox[
    StyleBox[
     RowBox[{"{", GridBox[{
        {
         RowBox[{
          RowBox[{
           SuperscriptBox["x", "2"], "+", "yz"}], "=", "1"}]},
        {
         RowBox[{
          RowBox[{"x", "+", 
           RowBox[{"2", "y"}]}], "\[LessEqual]", 
          RowBox[{
           RowBox[{"3", "z"}], "+", "1"}]}]},
        {
         RowBox[{"xyz", ">", "7"}]}
       }]}],
     ShowAutoStyles->False],
    #& ], TraditionalForm]], "None"],
 "\t"
}], "Subsection",
 CellChangeTimes->{{3.427653024754302*^9, 3.427653065355845*^9}, {
  3.427653866918251*^9, 3.427653913900872*^9}, {3.427778339934308*^9, 
  3.427778343671247*^9}, {3.459154022546875*^9, 3.459154024140625*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Reduce", "[", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"x", "^", "2"}], "+", 
       RowBox[{"y", " ", "z"}]}], "\[Equal]", "1"}], "&&", 
     RowBox[{
      RowBox[{"x", "+", 
       RowBox[{"2", "y"}]}], "\[LessEqual]", 
      RowBox[{
       RowBox[{"3", "z"}], "+", "1"}]}], "&&", 
     RowBox[{
      RowBox[{"x", " ", "y", " ", "z"}], ">", "7"}]}], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y", ",", "z"}], "}"}], ",", "Reals"}], "]"}], "//", 
  "N"}]], "Input",
 CellChangeTimes->{{3.42765282837475*^9, 3.427652828954577*^9}},
 CellID->91668569],

Cell[BoxData[
 RowBox[{
  RowBox[{"x", "<", 
   RowBox[{"-", "2.0867453398826665`"}]}], "&&", 
  RowBox[{"y", "<", "0.`"}], "&&", 
  RowBox[{"z", "\[Equal]", 
   FractionBox[
    RowBox[{"1.`", "\[InvisibleSpace]", "-", 
     RowBox[{"1.`", " ", 
      SuperscriptBox["x", "2"]}]}], "y"]}]}]], "Output",
 CellChangeTimes->{3.4591540300625*^9, 3.46156684821875*^9, 
  3.469795183921875*^9}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo 12\nHallar los valores reales de x e y que verifican:\n\t",
 Cell[BoxData[
  FormBox[
   StyleBox[
    RowBox[{"{", 
     StyleBox[GridBox[{
        {
         RowBox[{
          RowBox[{
           SuperscriptBox["3", "x"], "-", 
           SuperscriptBox["2", 
            RowBox[{"2", "y"}]]}], "=", "77"}]},
        {
         RowBox[{
          RowBox[{
           SqrtBox[
            SuperscriptBox["3", "x"]], "-", 
           SuperscriptBox["2", "y"]}], "=", "7"}]}
       }],
      ShowAutoStyles->True]}],
    ShowAutoStyles->False], TraditionalForm]]]
}], "Subsection",
 CellChangeTimes->{{3.427653024754302*^9, 3.427653065355845*^9}, {
  3.427653866918251*^9, 3.427653913900872*^9}, {3.4276539496715517`*^9, 
  3.4276540065633783`*^9}, {3.427654051648344*^9, 3.427654160589184*^9}, {
  3.427696298280943*^9, 3.4276963280219917`*^9}, {3.427696522928464*^9, 
  3.427696525307588*^9}, {3.427778383648695*^9, 3.4277783865568447`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Reduce", "[", " ", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      SuperscriptBox["3", "x"], "-", 
      SuperscriptBox["2", 
       RowBox[{"2", "y"}]]}], "\[Equal]", "77"}], " ", "&&", " ", 
    RowBox[{
     RowBox[{
      SqrtBox[
       SuperscriptBox["3", "x"]], "-", 
      SuperscriptBox["2", "y"]}], "\[Equal]", "7"}]}], ",", " ", 
   RowBox[{"{", 
    RowBox[{"x", ",", " ", "y"}], "}"}], ",", "Reals"}], "]"}]], "Input",
 CellChangeTimes->{3.4276540215792913`*^9},
 CellID->942160119],

Cell[BoxData[
 RowBox[{
  RowBox[{"x", "\[Equal]", "4"}], "&&", 
  RowBox[{"y", "\[Equal]", "1"}]}]], "Output",
 CellChangeTimes->{3.461566851140625*^9, 3.469795184625*^9}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo 13\nHallar los valores enteros  x , y, z que verifican:\n\t",
 Cell[BoxData[
  FormBox[
   StyleBox[
    RowBox[{"{", 
     StyleBox[GridBox[{
        {
         RowBox[{
          RowBox[{
           RowBox[{"2", "x"}], "+", 
           RowBox[{"3", "y"}], "-", 
           RowBox[{"5", "z"}]}], "=", "1"}]},
        {
         RowBox[{
          RowBox[{
           RowBox[{"3", "x"}], "-", 
           RowBox[{"4", "y"}], "+", 
           RowBox[{"7", "z"}]}], "=", "3"}]}
       }],
      ShowAutoStyles->True]}],
    ShowAutoStyles->False], TraditionalForm]]]
}], "Subsection",
 CellChangeTimes->{{3.427653024754302*^9, 3.427653065355845*^9}, {
  3.427653866918251*^9, 3.427653913900872*^9}, {3.4276539496715517`*^9, 
  3.4276540065633783`*^9}, {3.427654051648344*^9, 3.427654160589184*^9}, {
  3.427696286706781*^9, 3.42769638037156*^9}, {3.4276965304565496`*^9, 
  3.4276965320151567`*^9}, {3.4277783932809343`*^9, 3.427778395554337*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Reduce", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"2", " ", "x"}], "+", 
      RowBox[{"3", "y"}], "-", 
      RowBox[{"5", "z"}]}], "==", "1"}], "&&", 
    RowBox[{
     RowBox[{
      RowBox[{"3", "x"}], "-", 
      RowBox[{"4", "y"}], "+", 
      RowBox[{"7", "z"}]}], "\[Equal]", "3"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y", ",", "z"}], "}"}], ",", "Integers"}], 
  "]"}]], "Input",
 CellID->31436120],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"C", "[", "1", "]"}], "\[Element]", "Integers"}], "&&", 
  RowBox[{"x", "\[Equal]", 
   RowBox[{"C", "[", "1", "]"}]}], "&&", 
  RowBox[{"y", "\[Equal]", 
   RowBox[{"22", "-", 
    RowBox[{"29", " ", 
     RowBox[{"C", "[", "1", "]"}]}]}]}], "&&", 
  RowBox[{"z", "\[Equal]", 
   RowBox[{"13", "-", 
    RowBox[{"17", " ", 
     RowBox[{"C", "[", "1", "]"}]}]}]}]}]], "Output",
 CellChangeTimes->{3.461566851484375*^9, 3.469795184703125*^9}]
}, Open  ]],

Cell["\<\
En este resultado C[1] representa cualquier n\[UAcute]mero entero\
\>", "Text",
 CellChangeTimes->{{3.427696398296101*^9, 3.427696426298965*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo 14\nHallar los valores enteros de x que verifiquen:\n\ta) ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "1000"], "-", 
     RowBox[{"2", 
      SuperscriptBox["x", "777"]}], "+", "1"}], " ", "=", " ", "0"}], 
   TraditionalForm]], "None"],
 "\n\tb) ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "5"], "-", 
     RowBox[{"2", "x"}], "+", "1"}], "<", "0"}], TraditionalForm]], "None"]
}], "Subsection",
 CellChangeTimes->{{3.4276966077199802`*^9, 3.427696701079441*^9}, {
  3.4277784366929693`*^9, 3.427778438939822*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Reduce", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "1000"}], "-", 
     RowBox[{"2", 
      RowBox[{"x", "^", "777"}]}], "+", "1"}], "\[Equal]", "0"}], ",", "x", 
   ",", "Integers"}], "]"}]], "Input",
 CellID->626380406],

Cell[BoxData[
 RowBox[{"x", "\[Equal]", "1"}]], "Output",
 CellChangeTimes->{3.461566851515625*^9, 3.469795184734375*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Reduce", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", "5"}], "-", 
     RowBox[{"2", "x"}], "+", "1"}], "<", "0"}], ",", "x", ",", "Integers"}], 
  "]"}]], "Input",
 CellID->50212146],

Cell[BoxData[
 RowBox[{
  RowBox[{"x", "\[Element]", "Integers"}], "&&", 
  RowBox[{"x", "\[LessEqual]", 
   RowBox[{"-", "2"}]}]}]], "Output",
 CellChangeTimes->{3.461566851546875*^9, 3.469795184765625*^9}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
Ejemplo 15
Hallar todos los valores de x que verifican:
\tcos(x) = 1/2\
\>", "Subsection",
 CellChangeTimes->{{3.427697777015918*^9, 3.427697815260194*^9}, {
  3.427778492720381*^9, 3.427778494922214*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Reduce", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"Cos", "[", "x", "]"}], "\[Equal]", 
    RowBox[{"1", "/", "2"}]}], ",", "x"}], "]"}]], "Input",
 CellID->142038859],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"C", "[", "1", "]"}], "\[Element]", "Integers"}], "&&", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{"x", "\[Equal]", 
     RowBox[{
      RowBox[{"-", 
       FractionBox["\[Pi]", "3"]}], "+", 
      RowBox[{"2", " ", "\[Pi]", " ", 
       RowBox[{"C", "[", "1", "]"}]}]}]}], "||", 
    RowBox[{"x", "\[Equal]", 
     RowBox[{
      FractionBox["\[Pi]", "3"], "+", 
      RowBox[{"2", " ", "\[Pi]", " ", 
       RowBox[{"C", "[", "1", "]"}]}]}]}]}], ")"}]}]], "Output",
 CellChangeTimes->{3.46156685178125*^9, 3.46979518484375*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["  Sistemas de Ecuaciones Lineales", "Section 1"],

Cell[TextData[{
 "Sea el sistema lineal expresado en forma matricial:\n\tA.x = b\ndonde A es \
la matriz de los coeficientes, b es el vector de t\[EAcute]rminos \
independientes y x es el vector de las incognitas. si existe ",
 Cell[BoxData[
  SuperscriptBox["A", 
   RowBox[{"-", "1"}]]]],
 ", entonces la soluci\[OAcute]n del sistema es: \n\tx= ",
 Cell[BoxData[
  SuperscriptBox["A", 
   RowBox[{"-", "1"}]]]],
 "\t.b\n\nEsta es una forma de obtener la soluci\[OAcute]n del sistema. Tambi\
\[EAcute]n se pueden utilizar el comando Solve y el comando LinearSolve para \
resolver sistemas lineales.\t\n\nSiendo A la matriz de coeficientes y b el \
vector de t\[EAcute]rminos independientes, la sintaxis del comando \
LinearSolve es la siguiente:\n\tLinearSolve[A,b]"
}], "Text",
 CellChangeTimes->{{3.4276286012876453`*^9, 3.42762864753303*^9}, {
  3.45915414821875*^9, 3.459154210828125*^9}},
 TextAlignment->Left,
 TextJustification->1],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo 16\nResolver la ecuaci\[OAcute]n matricial y comprobar el resultado \
obtenido:\n\t",
 Cell[BoxData[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {"2", 
       RowBox[{"-", "1"}], "1"},
      {"4", "1", "1"},
      {"6", 
       RowBox[{"-", "6"}], "8"}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
        "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
   MatrixForm[#]& ]]],
 ".",
 Cell[BoxData[
  InterpretationBox[
   RowBox[{"(", GridBox[{
      {"x"},
      {"y"},
      {"z"}
     }], ")"}],
   MatrixForm[{x, y, z}]]]],
 " = ",
 Cell[BoxData[
  RowBox[{"(", "\[NoBreak]", 
   TagBox[GridBox[{
      {"1"},
      {"2"},
      {"3"}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
        "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.5599999999999999]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}],
    Column], "\[NoBreak]", ")"}]]]
}], "Subsection",
 CellChangeTimes->{
  3.427524152946485*^9, {3.427524185506216*^9, 3.427524193295944*^9}, 
   3.42754118171255*^9, {3.457932044796875*^9, 3.45793204496875*^9}, {
   3.4592356443125*^9, 3.459235666140625*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"A", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"2", ",", 
       RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"4", ",", "1", ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"6", ",", 
       RowBox[{"-", "6"}], ",", "8"}], "}"}]}], "}"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"b", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], ";"}]}], "Input",
 CellChangeTimes->{
  3.459154232921875*^9, {3.45923567859375*^9, 3.459235689296875*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"{", 
   RowBox[{"x", ",", "y", ",", "z"}], "}"}], "=", 
  RowBox[{
   RowBox[{"Inverse", "[", "A", "]"}], ".", "b"}]}]], "Input",
 CellChangeTimes->{3.459154240265625*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   FractionBox["1", "2"], ",", "0", ",", "0"}], "}"}]], "Output",
 CellChangeTimes->{3.45915425553125*^9, 3.459235694515625*^9, 
  3.461566852046875*^9, 3.469795184875*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"A", ".", 
  RowBox[{"{", 
   RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]], "Input",
 CellChangeTimes->{3.45915424425*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"1", ",", "2", ",", "3"}], "}"}]], "Output",
 CellChangeTimes->{3.459154258046875*^9, 3.459235700328125*^9, 
  3.461566852078125*^9, 3.46979518490625*^9}]
}, Open  ]],

Cell[TextData[{
 "Otra forma de resolver el sistema consiste en utilizar el comando ",
 StyleBox["Thread",
  FontWeight->"Bold"],
 ". al aplicar el comando ",
 StyleBox["Thread",
  FontWeight->"Bold"],
 " a matriza.{x,y,z}=={3,-1,4},  se obtiene {3 x+2 z==3,-3 x+2 y+2 z==-1,2 \
x-3 y+3 z==4}. \nAplicando el comando Solve a cualquiera de estos dos \
resultados se obtiene la soluci\[OAcute]n del sistema, pero parece mejor el \
primero que es como debe ir el argumento de Solve."
}], "Text",
 CellChangeTimes->{{3.427524283267989*^9, 3.427524332679995*^9}, {
  3.428129460578125*^9, 3.4281294725625*^9}},
 TextAlignment->Left,
 TextJustification->1],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", 
  RowBox[{"x", ",", "y", ",", "z"}], "]"}], "\n", 
 RowBox[{"sys", "=", 
  RowBox[{"Thread", "[", 
   RowBox[{
    RowBox[{"A", ".", 
     RowBox[{"{", 
      RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "==", 
    RowBox[{"{", 
     RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], "]"}]}]}], "Input",
 CellChangeTimes->{3.45915426596875*^9, 3.459235716265625*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"2", " ", "x"}], "-", "y", "+", "z"}], "\[Equal]", "1"}], ",", 
   RowBox[{
    RowBox[{
     RowBox[{"4", " ", "x"}], "+", "y", "+", "z"}], "\[Equal]", "2"}], ",", 
   RowBox[{
    RowBox[{
     RowBox[{"6", " ", "x"}], "-", 
     RowBox[{"6", " ", "y"}], "+", 
     RowBox[{"8", " ", "z"}]}], "\[Equal]", "3"}]}], "}"}]], "Output",
 CellChangeTimes->{3.459154270421875*^9, 3.459235719203125*^9, 
  3.461566852109375*^9, 3.4697951849375*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", "sys", "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"x", "\[Rule]", 
     FractionBox["1", "2"]}], ",", 
    RowBox[{"y", "\[Rule]", "0"}], ",", 
    RowBox[{"z", "\[Rule]", "0"}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.45915427203125*^9, 3.459235723140625*^9, 
  3.461566852140625*^9, 3.469795184984375*^9}]
}, Open  ]],

Cell["Finalmente con el comando Linearsolve", "Text",
 CellChangeTimes->{{3.459154275453125*^9, 3.45915428334375*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"LinearSolve", "[", 
  RowBox[{"A", ",", "b"}], "]"}]], "Input",
 CellChangeTimes->{{3.459154290296875*^9, 3.459154301296875*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   FractionBox["1", "2"], ",", "0", ",", "0"}], "}"}]], "Output",
 CellChangeTimes->{3.4591543026875*^9, 3.4592357265625*^9, 
  3.461566852171875*^9, 3.469795185015625*^9}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
Ejemplo 17
Resolver el sistema 
3x + y      =1
x + 2y+ z=-2
       y + z =4
Usando primero el comando RowReduce y despu\[EAcute]s el LinearSolve.\
\>", "Subsection",
 CellChangeTimes->{
  3.4275249464824343`*^9, {3.42752582336924*^9, 3.427525828914976*^9}, {
   3.427540574751431*^9, 3.427540592994253*^9}, {3.427541192273868*^9, 
   3.427541192939996*^9}, 3.45793204965625*^9, {3.45923580134375*^9, 
   3.45923587896875*^9}}],

Cell[TextData[{
 "Utilizaremos el comando ",
 StyleBox["ArrayFlatten",
  FontWeight->"Bold"],
 " para definir la matriz ampliada. En este caso es necesario introducir el \
vector b como un vector de tres filas y una columna de forma que tenga el \
mismo n\[UAcute]mero de filas que la matriz."
}], "Text",
 CellChangeTimes->{{3.427525613671055*^9, 3.4275256818092537`*^9}},
 TextAlignment->Left,
 TextJustification->1.],

Cell[BoxData[{
 RowBox[{
  RowBox[{"A", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"3", ",", "1", ",", "0"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"1", ",", "2", ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"0", ",", "1", ",", "1"}], "}"}]}], "}"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"b", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", 
     RowBox[{"-", "2"}], ",", "4"}], "}"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.4275251080699368`*^9, 3.427525129664156*^9}, {
   3.427525365566533*^9, 3.427525399333679*^9}, {3.45793169728125*^9, 
   3.457931705015625*^9}, 3.45915433325*^9, 3.459235795640625*^9, {
   3.45923588184375*^9, 3.459235889359375*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"ampli", "=", 
   RowBox[{"Transpose", "[", 
    RowBox[{"Append", "[", 
     RowBox[{
      RowBox[{"Transpose", "[", "A", "]"}], ",", "b"}], "]"}], "]"}]}], ";", 
  RowBox[{"MatrixForm", "[", "ampli", "]"}]}]], "Input",
 CellChangeTimes->{{3.427525480897601*^9, 3.427525509489931*^9}, {
   3.427525696845463*^9, 3.4275257241545877`*^9}, {3.4275257589504004`*^9, 
   3.427525777088023*^9}, {3.457931708984375*^9, 3.45793175653125*^9}, 
   3.459154338203125*^9}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"3", "1", "0", "1"},
     {"1", "2", "1", 
      RowBox[{"-", "2"}]},
     {"0", "1", "1", "4"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.459154340109375*^9, 3.4592358960625*^9, 
  3.461566852390625*^9, 3.469795185046875*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"?", "RowReduce"}]], "Input"],

Cell[BoxData[
 RowBox[{
  StyleBox["\<\"\!\(\*RowBox[{\\\"RowReduce\\\", \\\"[\\\", \
StyleBox[\\\"m\\\", \\\"TI\\\"], \\\"]\\\"}]\) gives the row\[Hyphen]reduced \
form of the matrix \!\(\*StyleBox[\\\"m\\\", \\\"TI\\\"]\). \"\>", "MSG"], 
  "\[NonBreakingSpace]", 
  ButtonBox[
   StyleBox["\[RightSkeleton]", "SR"],
   Active->True,
   BaseStyle->"Link",
   ButtonData->"paclet:ref/RowReduce"]}]], "Print", "PrintUsage",
 CellChangeTimes->{3.46979518525*^9},
 CellTags->"Info3469798785-8534086"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"RowReduce", "[", "ampli", "]"}], "//", "MatrixForm"}]], "Input",
 CellChangeTimes->{{3.427525744477046*^9, 3.4275257455469427`*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", 
      FractionBox["7", "2"]},
     {"0", "1", "0", 
      RowBox[{"-", 
       FractionBox["19", "2"]}]},
     {"0", "0", "1", 
      FractionBox["27", "2"]}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.459154348296875*^9, 3.459235901546875*^9, 
  3.461566852828125*^9, 3.469795185359375*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", 
  RowBox[{"x", ",", "y", ",", "z"}], "]"}], "\n", 
 RowBox[{
  RowBox[{"{", 
   RowBox[{
    RowBox[{
     RowBox[{"3", " ", "x"}], "+", "y"}], ",", " ", 
    RowBox[{"x", "+", 
     RowBox[{"2", " ", "y"}], "+", " ", "z"}], ",", " ", 
    RowBox[{"y", "+", " ", "z"}]}], "}"}], "/.", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"x", "\[Rule]", 
     RowBox[{"7", "/", "2"}]}], ",", 
    RowBox[{"y", "\[Rule]", 
     RowBox[{
      RowBox[{"-", "19"}], "/", "2"}]}], ",", 
    RowBox[{"z", "\[Rule]", 
     RowBox[{"27", "/", "2"}]}]}], "}"}]}]}], "Input",
 CellChangeTimes->{{3.45923592571875*^9, 3.45923599528125*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"1", ",", 
   RowBox[{"-", "2"}], ",", "4"}], "}"}]], "Output",
 CellChangeTimes->{
  3.45915435509375*^9, {3.4592359809375*^9, 3.459235996765625*^9}, 
   3.461566852875*^9, 3.469795185390625*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"LinearSolve", "[", 
  RowBox[{"A", ",", "b"}], "]"}]], "Input",
 CellChangeTimes->{{3.428129537703125*^9, 3.428129558984375*^9}, 
   3.459154359953125*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   FractionBox["7", "2"], ",", 
   RowBox[{"-", 
    FractionBox["19", "2"]}], ",", 
   FractionBox["27", "2"]}], "}"}]], "Output",
 CellChangeTimes->{3.45915436115625*^9, 3.45923600028125*^9, 
  3.4615668529375*^9, 3.4697951854375*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"A", ".", 
     RowBox[{"{", 
      RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "\[Equal]", "b"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.457931787921875*^9, 3.45793182834375*^9}, 
   3.4591543641875*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"x", "\[Rule]", 
     FractionBox["7", "2"]}], ",", 
    RowBox[{"y", "\[Rule]", 
     RowBox[{"-", 
      FractionBox["19", "2"]}]}], ",", 
    RowBox[{"z", "\[Rule]", 
     FractionBox["27", "2"]}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.45915436565625*^9, 3.459236003921875*^9, 
  3.461566852984375*^9, 3.469795185484375*^9}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
Ejemplo 18
Resolver el sistema:
x + y + z =1
2x - y +3z=4
3x + 2y - 2z=2
igual que en el ejercicio anterior.\
\>", "Subsection",
 CellChangeTimes->{
  3.4275257965227127`*^9, {3.427525837994946*^9, 3.4275258445797243`*^9}, {
   3.4275406287719307`*^9, 3.42754063744*^9}, 3.427541205429303*^9, 
   3.457932055328125*^9, {3.459236077109375*^9, 3.45923613921875*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"aument", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"1", ",", "1", ",", "1", ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"2", ",", 
       RowBox[{"-", "1"}], ",", "3", ",", "4"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"3", ",", "2", ",", 
       RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], ";"}], "\n", 
 RowBox[{"RowReduce", "[", "aument", "]"}]}], "Input",
 CellChangeTimes->{{3.45923605884375*^9, 3.459236072484375*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1", ",", "0", ",", "0", ",", 
     FractionBox["5", "4"]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "1", ",", "0", ",", 
     RowBox[{"-", 
      FractionBox["9", "16"]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "1", ",", 
     FractionBox["5", "16"]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.45915437053125*^9, 3.45923614115625*^9, 
  3.46156685303125*^9, 3.46979518553125*^9}]
}, Open  ]],

Cell[BoxData[{
 RowBox[{"Clear", "[", 
  RowBox[{"x", ",", "y", ",", "z"}], "]"}], "\n", 
 RowBox[{
  RowBox[{"eq1", "=", 
   RowBox[{
    RowBox[{"x", "+", "y", "+", "z"}], "\[Equal]", "1"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"eq2", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"2", "x"}], "-", "y", "+", 
     RowBox[{"3", "z"}]}], "\[Equal]", "4"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"eq3", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"3", "x"}], "+", 
     RowBox[{"2", "y"}], "-", 
     RowBox[{"2", "z"}]}], "\[Equal]", "2"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.459236147953125*^9, 3.45923621953125*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"x", "=", 
   RowBox[{"5", "/", "4"}]}], ";", 
  RowBox[{"y", "=", 
   RowBox[{
    RowBox[{"-", "9"}], "/", "16"}]}], ";", 
  RowBox[{"z", "=", 
   RowBox[{"5", "/", "16"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.459236235984375*^9, 3.459236250453125*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"eq1", ",", "eq2", ",", "eq3"}], "}"}]], "Input"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"True", ",", "True", ",", "True"}], "}"}]], "Output",
 CellChangeTimes->{3.45915437815625*^9, 3.45923625378125*^9, 
  3.461566853078125*^9, 3.469795185578125*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"LinearSolve", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"1", ",", "1", ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"2", ",", 
       RowBox[{"-", "1"}], ",", "3"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"3", ",", "2", ",", 
       RowBox[{"-", "2"}]}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1", ",", "4", ",", "2"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.428129604359375*^9, 3.42812965753125*^9}, {
  3.45923627659375*^9, 3.459236287890625*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   FractionBox["5", "4"], ",", 
   RowBox[{"-", 
    FractionBox["9", "16"]}], ",", 
   FractionBox["5", "16"]}], "}"}]], "Output",
 CellChangeTimes->{3.459154380828125*^9, 3.45923628953125*^9, 
  3.461566853109375*^9, 3.469795185609375*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
WindowToolbars->{"RulerBar", "EditBar"},
WindowSize->{1672, 933},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
DockedCells->FEPrivate`If[
  FEPrivate`SameQ[FEPrivate`$ProductIDName, "MathematicaPlayer"], 
  FEPrivate`Join[{
    Cell[
     BoxData[
      GraphicsBox[
       RasterBox[CompressedData["
1:eJztXXdYFNfaz3O/f+79vudek3vTLKBIEaQpTRC7BgtqLCTWGxNjYsFookE0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        "], {{0, 0}, {557, 41}}, {0, 255}, ColorFunction -> RGBColor], 
       ImageSize -> {557, 41}, PlotRange -> {{0, 557}, {0, 41}}]], 
     "DockedCell", Background -> GrayLevel[0.866682], 
     CellFrame -> {{0, 0}, {0, 4}}, CellFrameColor -> 
     RGBColor[0.690074, 0.12871, 0.194598], CellMargins -> {{0, 0}, {-3, 0}}, 
     CellFrameMargins -> 0, ContextMenu -> None, 
     ComponentwiseContextMenu -> {}], 
    Cell[
     BoxData[
      GridBox[{{
         GraphicsBox[
          RasterBox[CompressedData["
1:eJztWl1Ik1EYFrqNEoLMbHPmNkRrEhJERj93ra4cJvbDRIsyMk1pc03tTL1w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           "], {{0, 0}, {199, 30}}, {0, 255}, ColorFunction -> RGBColor], 
          ImageSize -> {199, 30}, PlotRange -> {{0, 199}, {0, 30}}], 
         ButtonBox[
          GraphicsBox[
           RasterBox[CompressedData["
1:eJztlDFuhFAMRJHS5w45Re6RI+wFcoOUtNtR0lJSUlNSUtNS0m9JXjTKaPQh
UfpgCeT1n2+Px15ebu9vt6eqqp55Xnm+/I/L/p+1bbtt277vvJumIcKbnwWs
73vBsHVdE1bXNQ55Ho8HMOEd3L9tWRZ+6tRBrrjEMAwigHO/37M6SII40zRB
Q7QLkpQWjKOu63RqGHHVIoOYYAR16oucinYGxUo2jqMIzPNMnpQRPF2nMkeS
cCBDXsm7ZNZp6oZRS3wsIBFNIYM2iY8gYmJA8imqawHcOAKqio4KSp4O7Qjp
K1nOUygasaG2hoKSaud3krkArggZzyhhTohP3Uz7E0mNu9g98oj26exOSTon
fRUtn8IUJL+W80gyuz6OW3mgrSXXEv5dSaRTaRz9KQpY/knxtVomKdFQxvFT
JZFR6pFBJWT5tbEvR9+H3F6S+GOSMC+DTHtrHYyh32Qu855cdhn2CUundjY=

            "], {{0, 0}, {55, 14}}, {0, 255}, ColorFunction -> RGBColor], 
           ImageSize -> {55, 14}, PlotRange -> {{0, 55}, {0, 14}}], 
          ButtonData -> {
            URL["http://store.wolfram.com/view/app/playerpro/"], None}, 
          ButtonNote -> "http://store.wolfram.com/view/app/playerpro/"], 
         GraphicsBox[
          
          RasterBox[{{{132, 132, 132}, {156, 155, 155}}, {{138, 137, 137}, {
           171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 
           137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 
           137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{
           138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 
           169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 
           169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {
           171, 169, 169}}, {{135, 135, 135}, {167, 166, 166}}}, {{0, 0}, {2, 
           14}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {2, 14}, 
          PlotRange -> {{0, 2}, {0, 14}}], 
         ButtonBox[
          GraphicsBox[
           RasterBox[CompressedData["
1:eJztlSGSg2AMhTuzfu+wB1qzR+gF9gbIWhwSW4lEV1ZWYyvxSPZb3vAmDdDq
zpCZdvKH5CUvfwhfx9+f48fhcPjk983vXy922eU9paqqcRx9HGcZhiE+PZ1O
KHVd24KOgt0WFKLQ27ZdJrper0JGcS5CVqs6n89yRpGl73tZBK6kkvv97kCe
ChOlLEvbVW2kiYPoxKcYRdwWld00jS2EcFSFMYXCqbOcBJzL5aJcxK7SFEFB
GQFn8AWupPUkMRfIJEK53W5d1z2hGVP7yohVbfanWoxAJQTfeywbT1+xK9mi
GQGTj8FT0uRAN3Tdjl3SlNANP5WoabIIRP+x52ojLEgXs8fxs7+R1cCXNFH6
SVJhKZwx0+BxBZ7nraGNpBSrEFlA1khgRDcCRg1navIWTeVKPVmliaeaL+c4
tCmcknRHfjtWaS6HNtYmC1wYjGJ+6eKjJcficWgVssz1nGbabFtD682gZaIO
MHXqkq/vyW3GFaQXliNuOhbz9lOHU3a6SrhWkCmnXC9pUoPBt1aQpquYrtJt
0f6Pazkd497W1MkSlxierkrrN254iz8oHqS0ByzxGzfOHx2yq9plYSl8l13e
Xf4ArlmHrg==
            "], {{0, 0}, {77, 14}}, {0, 255}, ColorFunction -> RGBColor], 
           ImageSize -> {77, 14}, PlotRange -> {{0, 77}, {0, 14}}], 
          ButtonData -> {
            URL[
            "http://www.wolfram.com/solutions/interactivedeployment/\
licensingterms.html"], None}, ButtonNote -> 
          "http://www.wolfram.com/solutions/interactivedeployment/\
licensingterms.html"]}}, ColumnsEqual -> False, 
       GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}]], 
     "DockedCell", Background -> GrayLevel[0.494118], 
     CellFrame -> {{0, 0}, {4, 0}}, CellFrameColor -> 
     RGBColor[0.690074, 0.12871, 0.194598], CellMargins -> 0, 
     CellFrameMargins -> {{0, 0}, {0, -1}}, ContextMenu -> None, 
     ComponentwiseContextMenu -> {}, 
     ButtonBoxOptions -> {ButtonFunction :> (FrontEndExecute[{
          NotebookLocate[#2]}]& ), Appearance -> None, ButtonFrame -> None, 
       Evaluator -> None, Method -> "Queued"}]}, 
   FEPrivate`If[
    FEPrivate`SameQ[
     FrontEnd`CurrentValue[
      FrontEnd`EvaluationNotebook[], ScreenStyleEnvironment], "SlideShow"], {
    Inherited}, {}]], Inherited],
PrintingCopies->1,
PrintingPageRange->{1, 1},
PrivateNotebookOptions->{"ColorPalette"->{RGBColor, 128}},
ShowSelection->True,
ShowCellLabel->False,
ShowCellTags->False,
RenderingOptions->{"ObjectDithering"->True,
"RasterDithering"->False},
Magnification->1.5,
FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (November 10, 2008)",
StyleDefinitions->"Report.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
 "Info3469798779-9406029"->{
  Cell[1788, 59, 534, 12, 93, "Print",
   CellTags->"Info3469798779-9406029"]},
 "Info3469798780-6240857"->{
  Cell[2410, 79, 936, 18, 132, "Print",
   CellTags->"Info3469798780-6240857"]},
 "Info3469798782-9119275"->{
  Cell[45180, 1359, 711, 15, 93, "Print",
   CellTags->"Info3469798782-9119275"]},
 "Info3469798785-8534086"->{
  Cell[147526, 3955, 498, 12, 93, "Print",
   CellTags->"Info3469798785-8534086"]}
 }
*)
(*CellTagsIndex
CellTagsIndex->{
 {"Info3469798779-9406029", 171724, 4517},
 {"Info3469798780-6240857", 171833, 4520},
 {"Info3469798782-9119275", 171943, 4523},
 {"Info3469798785-8534086", 172055, 4526}
 }
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[567, 22, 359, 7, 241, "Subtitle"],
Cell[CellGroupData[{
Cell[951, 33, 133, 1, 153, "Section 1"],
Cell[1087, 36, 628, 16, 91, "Text"],
Cell[CellGroupData[{
Cell[1740, 56, 45, 1, 69, "Input"],
Cell[1788, 59, 534, 12, 93, "Print",
 CellTags->"Info3469798779-9406029"]
}, Open  ]],
Cell[CellGroupData[{
Cell[2359, 76, 48, 1, 69, "Input"],
Cell[2410, 79, 936, 18, 132, "Print",
 CellTags->"Info3469798780-6240857"]
}, Open  ]],
Cell[CellGroupData[{
Cell[3383, 102, 470, 16, 262, "Subsection"],
Cell[CellGroupData[{
Cell[3878, 122, 215, 6, 69, "Input"],
Cell[4096, 130, 181, 5, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4314, 140, 278, 8, 115, "Input"],
Cell[4595, 150, 184, 5, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4816, 160, 232, 6, 76, "Input"],
Cell[5051, 168, 409, 12, 102, "Output"]
}, Open  ]],
Cell[5475, 183, 1029, 21, 160, "Text"],
Cell[CellGroupData[{
Cell[6529, 208, 284, 9, 115, "Input"],
Cell[6816, 219, 208, 6, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[7061, 230, 159, 4, 69, "Input"],
Cell[7223, 236, 131, 3, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[7391, 244, 236, 7, 76, "Input"],
Cell[7630, 253, 434, 13, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[8101, 271, 129, 4, 69, "Input"],
Cell[8233, 277, 134, 3, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[8404, 285, 129, 4, 69, "Input"],
Cell[8536, 291, 148, 3, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[8721, 299, 194, 5, 69, "Input"],
Cell[8918, 306, 149, 3, 102, "Output"]
}, Open  ]],
Cell[9082, 312, 530, 11, 126, "Text"],
Cell[CellGroupData[{
Cell[9637, 327, 214, 6, 69, "Input"],
Cell[9854, 335, 692, 13, 70, "Message"],
Cell[10549, 350, 206, 5, 102, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[10804, 361, 379, 11, 124, "Subsection"],
Cell[CellGroupData[{
Cell[11208, 376, 311, 9, 69, "Input"],
Cell[11522, 387, 673, 12, 70, "Message"],
Cell[12198, 401, 450, 14, 132, "Output"]
}, Open  ]],
Cell[12663, 418, 1065, 22, 195, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[13765, 445, 798, 27, 225, "Subsection"],
Cell[CellGroupData[{
Cell[14588, 476, 90, 1, 61, "Subsubsection"],
Cell[CellGroupData[{
Cell[14703, 481, 519, 16, 76, "Input"],
Cell[15225, 499, 1166, 31, 141, "Output"]
}, Open  ]],
Cell[16406, 533, 331, 6, 91, "Text"],
Cell[CellGroupData[{
Cell[16762, 543, 785, 23, 76, "Input"],
Cell[17550, 568, 5763, 101, 882, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[23362, 675, 89, 1, 61, "Subsubsection"],
Cell[23454, 678, 322, 5, 91, "Text"],
Cell[CellGroupData[{
Cell[23801, 687, 537, 16, 115, "Input"],
Cell[24341, 705, 946, 32, 141, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[25324, 742, 1010, 28, 115, "Input"],
Cell[26337, 772, 1787, 36, 1078, "Output"]
}, Open  ]],
Cell[28139, 811, 940, 19, 160, "Text"],
Cell[CellGroupData[{
Cell[29104, 834, 296, 10, 76, "Input",
 CellID->1497],
Cell[29403, 846, 2131, 68, 156, "Output"]
}, Open  ]],
Cell[31549, 917, 306, 6, 57, "Text"],
Cell[CellGroupData[{
Cell[31880, 927, 301, 10, 76, "Input",
 CellID->1007333637],
Cell[32184, 939, 1365, 33, 141, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[33586, 977, 342, 11, 76, "Input"],
Cell[33931, 990, 1365, 33, 141, "Output"]
}, Open  ]],
Cell[35311, 1026, 232, 4, 57, "Text"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[35592, 1036, 426, 16, 204, "Subsection"],
Cell[CellGroupData[{
Cell[36043, 1056, 237, 8, 76, "Input"],
Cell[36283, 1066, 676, 16, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[36996, 1087, 213, 7, 76, "Input"],
Cell[37212, 1096, 576, 16, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[37825, 1117, 204, 7, 76, "Input"],
Cell[38032, 1126, 674, 16, 102, "Output"]
}, Open  ]],
Cell[38721, 1145, 424, 10, 57, "Text"],
Cell[CellGroupData[{
Cell[39170, 1159, 295, 8, 69, "Input"],
Cell[39468, 1169, 573, 20, 124, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[40102, 1196, 203, 4, 153, "Section 1"],
Cell[40308, 1202, 649, 15, 91, "Text"],
Cell[CellGroupData[{
Cell[40982, 1221, 263, 8, 201, "Subsection"],
Cell[CellGroupData[{
Cell[41270, 1233, 502, 17, 69, "Input",
 CellID->539162013],
Cell[41775, 1252, 192, 5, 102, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[42028, 1264, 115, 3, 153, "Section 1"],
Cell[42146, 1269, 802, 15, 126, "Text"],
Cell[CellGroupData[{
Cell[42973, 1288, 562, 15, 159, "Subsection"],
Cell[CellGroupData[{
Cell[43560, 1307, 365, 12, 76, "Input"],
Cell[43928, 1321, 938, 21, 141, "Output"]
}, Open  ]],
Cell[44881, 1345, 226, 7, 57, "Text"],
Cell[CellGroupData[{
Cell[45132, 1356, 45, 1, 69, "Input"],
Cell[45180, 1359, 711, 15, 93, "Print",
 CellTags->"Info3469798782-9119275"]
}, Open  ]],
Cell[CellGroupData[{
Cell[45928, 1379, 342, 11, 76, "Input"],
Cell[46273, 1392, 1152, 30, 141, "Output"]
}, Open  ]],
Cell[47440, 1425, 1059, 23, 126, "Text"],
Cell[CellGroupData[{
Cell[48524, 1452, 417, 13, 76, "Input"],
Cell[48944, 1467, 10845, 183, 573, "Output"]
}, Open  ]],
Cell[59804, 1653, 242, 4, 57, "Text"],
Cell[CellGroupData[{
Cell[60071, 1661, 412, 13, 76, "Input"],
Cell[60486, 1676, 180, 4, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[60703, 1685, 441, 14, 76, "Input"],
Cell[61147, 1701, 180, 4, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[61364, 1710, 391, 12, 76, "Input"],
Cell[61758, 1724, 161, 3, 102, "Output"]
}, Open  ]],
Cell[61934, 1730, 364, 7, 57, "Text"],
Cell[CellGroupData[{
Cell[62323, 1741, 465, 15, 76, "Input"],
Cell[62791, 1758, 262, 7, 102, "Output"]
}, Open  ]],
Cell[63068, 1768, 516, 10, 91, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[63621, 1783, 226, 6, 162, "Subsection"],
Cell[CellGroupData[{
Cell[63872, 1793, 349, 11, 151, "Input"],
Cell[64224, 1806, 2124, 40, 537, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[66385, 1851, 190, 6, 69, "Input"],
Cell[66578, 1859, 159, 3, 102, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[66786, 1868, 446, 13, 168, "Subsection"],
Cell[67235, 1883, 355, 7, 57, "Text"],
Cell[CellGroupData[{
Cell[67615, 1894, 1078, 33, 235, "Input"],
Cell[68696, 1929, 27942, 465, 553, "Output"]
}, Open  ]],
Cell[96653, 2397, 400, 9, 57, "Text"],
Cell[CellGroupData[{
Cell[97078, 2410, 315, 9, 69, "Input"],
Cell[97396, 2421, 155, 3, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[97588, 2429, 75, 2, 69, "Input"],
Cell[97666, 2433, 110, 1, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[97813, 2439, 83, 2, 69, "Input"],
Cell[97899, 2443, 110, 1, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[98046, 2449, 315, 9, 69, "Input"],
Cell[98364, 2460, 159, 3, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[98560, 2468, 75, 2, 69, "Input"],
Cell[98638, 2472, 107, 1, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[98782, 2478, 83, 2, 69, "Input"],
Cell[98868, 2482, 110, 1, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[99015, 2488, 311, 9, 69, "Input"],
Cell[99329, 2499, 158, 3, 102, "Output"]
}, Open  ]],
Cell[99502, 2505, 315, 5, 57, "Text"],
Cell[CellGroupData[{
Cell[99842, 2514, 590, 20, 69, "Input",
 CellID->85154930],
Cell[100435, 2536, 309, 7, 102, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[100783, 2548, 142, 3, 153, "Section 1"],
Cell[CellGroupData[{
Cell[100950, 2555, 112, 1, 85, "Section"],
Cell[101065, 2558, 834, 18, 229, "Text"],
Cell[101902, 2578, 898, 30, 172, "Text"],
Cell[CellGroupData[{
Cell[102825, 2612, 560, 18, 69, "Input",
 CellID->47420189],
Cell[103388, 2632, 622, 21, 154, "Output"]
}, Open  ]],
Cell[104025, 2656, 855, 28, 172, "Text"],
Cell[CellGroupData[{
Cell[104905, 2688, 589, 18, 69, "Input",
 CellID->60662809],
Cell[105497, 2708, 405, 13, 132, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[105939, 2726, 633, 14, 201, "Subsection"],
Cell[106575, 2742, 373, 7, 91, "Text"],
Cell[CellGroupData[{
Cell[106973, 2753, 465, 13, 69, "Input"],
Cell[107441, 2768, 483, 16, 132, "Output"]
}, Open  ]],
Cell[107939, 2787, 176, 3, 69, "Input"],
Cell[CellGroupData[{
Cell[108140, 2794, 196, 5, 69, "Input"],
Cell[108339, 2801, 355, 12, 132, "Output"]
}, Open  ]],
Cell[108709, 2816, 638, 18, 69, "Input"],
Cell[109350, 2836, 304, 8, 69, "Input"],
Cell[CellGroupData[{
Cell[109679, 2848, 152, 3, 69, "Input"],
Cell[109834, 2853, 12266, 209, 1044, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[122161, 3069, 103, 1, 147, "Section"],
Cell[122267, 3072, 800, 16, 195, "Text"],
Cell[123070, 3090, 351, 10, 60, "Text"],
Cell[CellGroupData[{
Cell[123446, 3104, 251, 9, 69, "Input",
 CellID->15483236],
Cell[123700, 3115, 352, 12, 120, "Output"]
}, Open  ]],
Cell[124067, 3130, 386, 12, 60, "Text"],
Cell[CellGroupData[{
Cell[124478, 3146, 452, 14, 69, "Input",
 CellID->118871955],
Cell[124933, 3162, 294, 10, 154, "Output"]
}, Open  ]],
Cell[125242, 3175, 293, 9, 60, "Text"],
Cell[CellGroupData[{
Cell[125560, 3188, 283, 9, 69, "Input",
 CellID->758827168],
Cell[125846, 3199, 658, 22, 144, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[126541, 3226, 494, 14, 124, "Subsection"],
Cell[CellGroupData[{
Cell[127060, 3244, 323, 10, 69, "Input",
 CellID->223254230],
Cell[127386, 3256, 942, 32, 138, "Output"]
}, Open  ]],
Cell[128343, 3291, 1049, 36, 211, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[129429, 3332, 797, 26, 240, "Subsection"],
Cell[CellGroupData[{
Cell[130251, 3362, 622, 20, 69, "Input",
 CellID->91668569],
Cell[130876, 3384, 389, 11, 144, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[131314, 3401, 969, 27, 216, "Subsection"],
Cell[CellGroupData[{
Cell[132308, 3432, 528, 17, 97, "Input",
 CellID->942160119],
Cell[132839, 3451, 172, 4, 102, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[133060, 3461, 971, 27, 195, "Subsection"],
Cell[CellGroupData[{
Cell[134056, 3492, 472, 17, 69, "Input",
 CellID->31436120],
Cell[134531, 3511, 488, 14, 102, "Output"]
}, Open  ]],
Cell[135034, 3528, 155, 3, 57, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[135226, 3536, 611, 19, 201, "Subsection"],
Cell[CellGroupData[{
Cell[135862, 3559, 268, 9, 69, "Input",
 CellID->626380406],
Cell[136133, 3570, 121, 2, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[136291, 3577, 227, 8, 69, "Input",
 CellID->50212146],
Cell[136521, 3587, 207, 5, 102, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[136777, 3598, 215, 6, 162, "Subsection"],
Cell[CellGroupData[{
Cell[137017, 3608, 190, 6, 69, "Input",
 CellID->142038859],
Cell[137210, 3616, 574, 17, 127, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[137845, 3640, 54, 0, 153, "Section 1"],
Cell[137902, 3642, 939, 20, 339, "Text"],
Cell[CellGroupData[{
Cell[138866, 3666, 1707, 55, 229, "Subsection"],
Cell[140576, 3723, 563, 18, 111, "Input"],
Cell[CellGroupData[{
Cell[141164, 3745, 206, 6, 69, "Input"],
Cell[141373, 3753, 212, 5, 132, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[141622, 3763, 144, 4, 69, "Input"],
Cell[141769, 3769, 193, 4, 102, "Output"]
}, Open  ]],
Cell[141977, 3776, 650, 15, 91, "Text"],
Cell[CellGroupData[{
Cell[142652, 3795, 398, 11, 111, "Input"],
Cell[143053, 3808, 520, 15, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[143610, 3828, 60, 1, 69, "Input"],
Cell[143673, 3831, 334, 9, 132, "Output"]
}, Open  ]],
Cell[144022, 3843, 118, 1, 57, "Text"],
Cell[CellGroupData[{
Cell[144165, 3848, 153, 3, 69, "Input"],
Cell[144321, 3853, 212, 5, 132, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[144582, 3864, 436, 12, 277, "Subsection"],
Cell[145021, 3878, 419, 10, 91, "Text"],
Cell[145443, 3890, 704, 19, 111, "Input"],
Cell[CellGroupData[{
Cell[146172, 3913, 496, 11, 69, "Input"],
Cell[146671, 3926, 763, 21, 159, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[147471, 3952, 52, 1, 69, "Input"],
Cell[147526, 3955, 498, 12, 93, "Print",
 CellTags->"Info3469798785-8534086"]
}, Open  ]],
Cell[CellGroupData[{
Cell[148061, 3972, 167, 3, 69, "Input"],
Cell[148231, 3977, 843, 24, 226, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[149111, 4006, 657, 20, 111, "Input"],
Cell[149771, 4028, 235, 6, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[150043, 4039, 179, 4, 69, "Input"],
Cell[150225, 4045, 276, 8, 132, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[150538, 4058, 348, 10, 69, "Input"],
Cell[150889, 4070, 406, 12, 132, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[151344, 4088, 374, 11, 277, "Subsection"],
Cell[CellGroupData[{
Cell[151743, 4103, 514, 14, 111, "Input"],
Cell[152260, 4119, 493, 14, 132, "Output"]
}, Open  ]],
Cell[152768, 4136, 620, 20, 192, "Input"],
Cell[153391, 4158, 293, 9, 69, "Input"],
Cell[CellGroupData[{
Cell[153709, 4171, 88, 2, 69, "Input"],
Cell[153800, 4175, 201, 4, 102, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[154038, 4184, 553, 16, 69, "Input"],
Cell[154594, 4202, 281, 8, 132, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}
]
*)

(* End of internal cache information *)
(* NotebookSignature 5u0ksqOaF7kr2B1#Br052ngK *)