(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 31642, 812] NotebookOptionsPosition[ 13624, 462] NotebookOutlinePosition[ 30204, 760] CellTagsIndexPosition[ 30161, 757] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ TAREA 5\.aa: RESOLUCION DE ECUACIONES E INCECUACIONES\ \>", "Title", CellChangeTimes->{ 3.42813469284375*^9, {3.428826521171875*^9, 3.428826525078125*^9}, 3.4644343661708765`*^9}, TextAlignment->Center, TextJustification->0], Cell[CellGroupData[{ Cell[TextData[{ "Ejercicio 1\nRepresentar gr\[AAcute]ficamente en el plano complejo las \ raices del polinomio:\n\t5", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["x", "5"], "+", RowBox[{"4", SuperscriptBox["x", "3"]}], "+", "x", "+", "1"}], TraditionalForm]], "None"] }], "Subsection", CellChangeTimes->{{3.427693724979268*^9, 3.427693816417029*^9}, { 3.427777503849399*^9, 3.427777504132401*^9}, {3.464434380999002*^9, 3.4644343824521265`*^9}}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.42866803728125*^9}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Ejercicio 2 Resolver los siguientes sistemas de ecuaciones: a) 2x-6y+8z=24, 5x+4y-3z=2, 3x+y+2z=16 . b) 4x+2y+z=11, -x+2y=3, 2x+y+4z=16. c) 2x+5y+5z=12, 5x+2y+5z=12, 5x+5y+2z=12. d) -x+11y-z+3t=25, 2x-y+10z-t=-11, 10x-y+2z=6, 3y-z+8t=15.\ \>", "Subsection", CellChangeTimes->{{3.427777523843512*^9, 3.427777524285412*^9}, { 3.464434405436502*^9, 3.464434438842752*^9}, {3.464434487874002*^9, 3.4644346537958765`*^9}}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.42866806146875*^9}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Ejercicio 3\nSean las funciones h(x) = ", Cell[BoxData[ RowBox[{ SuperscriptBox["x", "3"], "-", RowBox[{"2", SuperscriptBox["x", "2"]}], "+", RowBox[{"3", "x"}], "-", "7"}]]], " y k(x) = ", Cell[BoxData[ RowBox[{ SuperscriptBox["x", "2"], "+", "x", "-", "1"}]]], ".\nAproximar las ra\[IAcute]ces reales de la ecuaci\[OAcute]n h(x) = k(x) \ utilizando los comandos NSolve y NRoots.\nCrear una lista que contenga los \ puntos de corte de las curvas y=h(x) e y=k(x)" }], "Subsection", CellChangeTimes->{{3.427777530773946*^9, 3.427777532083507*^9}, { 3.464434667655252*^9, 3.4644347673583765`*^9}}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.428668073296875*^9}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Ejercicio 4\nAproximar las soluciones del sistema de ecuaciones:\n", Cell[BoxData[{ FormBox[ RowBox[{ RowBox[{ SuperscriptBox["x", "2"], "+", RowBox[{"2", "x"}], "+", SuperscriptBox["y", "2"], "+", RowBox[{"2", "y"}], "+", "1"}], "=", "0"}], TraditionalForm], "\[IndentingNewLine]", FormBox[ RowBox[{ RowBox[{ SuperscriptBox["x", "2"], "-", SuperscriptBox["y", "2"]}], "=", FractionBox["1", "4"]}], TraditionalForm]}], FormatType->"TraditionalForm"], "\nUtilizar el comando ContourPlot para representar gr\[AAcute]ficamente las \ dos curvas y obtener unas aproximaciones de las soluciones del sistema." }], "Subsection", CellChangeTimes->{{3.42777754211094*^9, 3.427777544179324*^9}, { 3.4644347777333765`*^9, 3.464434818811502*^9}, {3.464434899280252*^9, 3.4644349628896265`*^9}}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.4286680900625*^9}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Ejercicio 5\nEliminar z en el sistema de ecuaciones,\n\t", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"], "+", SuperscriptBox["z", "2"], " "}], TraditionalForm]], "None"], "= 1\n\tx-y+z = 2\n\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SuperscriptBox["x", "3"], "-", SuperscriptBox["y", "2"]}], " ", "=", " ", RowBox[{"z", "+", "1"}]}], TraditionalForm]], "None"] }], "Subsection", CellChangeTimes->{{3.427519495121357*^9, 3.4275195171945143`*^9}, { 3.427519594378459*^9, 3.427519673742333*^9}, {3.427520188941381*^9, 3.427520327450708*^9}, {3.427778010021956*^9, 3.427778015490127*^9}, 3.4644350139208765`*^9}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.42866810690625*^9}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Ejercicio 6\nObtener los puntos de intersecci\[OAcute]n de dos curvas, h(x) \ = ", Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", SuperscriptBox["x", "2"]}], "+", RowBox[{"12", "x"}], "-", "5"}]]], " y \nk(x) = ", Cell[BoxData[ RowBox[{ RowBox[{"2", SuperscriptBox["x", "2"]}], "-", RowBox[{"4", "x"}], "-", "3"}]]], "." }], "Subsection", CellChangeTimes->{{3.427521332311223*^9, 3.4275213335044193`*^9}, 3.4277780852368937`*^9, {3.427778119365777*^9, 3.4277781249123383`*^9}, 3.464435016030252*^9}, TextAlignment->Left, TextJustification->1], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.4286681255*^9}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Ejercicio 7\nObtener una pareja de valores enteros {x,y} que verifique:\n", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SuperscriptBox["x", "2"], "-", RowBox[{"3", SuperscriptBox["y", "2"]}]}], "=", "1"}], TraditionalForm]], "None"], " con 10 < x < 100.\nComprobar gr\[AAcute]ficamente que la \ soluci\[OAcute]n obtenida verifica el sistema.\nRepetir el ejercicio \ obteniendo 3 puntos de la soluci\[OAcute]n." }], "Subsection", CellChangeTimes->{{3.427649727404915*^9, 3.427649834640563*^9}, { 3.4276507360065002`*^9, 3.427650790638932*^9}, {3.427778216929162*^9, 3.42777821763461*^9}, 3.464435018374002*^9}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.428668138671875*^9}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Ejercicio 8\n1\.ba.- Encontrar el conjunto de valores de x, y, z que \ verifica:\n\t", Cell[BoxData[ FormBox[ TagBox[ 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]]], "\n2\.ba.- Hallar las raices de la ecuaci\[OAcute]n : ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SuperscriptBox["x", "3"], "-", RowBox[{"2", "x"}], "+", "1"}], "=", "0"}], TraditionalForm]], "None"], " utilizando el comando Reduce.\n3\.ba.- Hallar las raices reales de la \ ecuaci\[OAcute]n : ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SuperscriptBox["x", "5"], "-", RowBox[{"2", "x"}], "+", "1"}], "=", "0"}], TraditionalForm]], "None"], " utilizando el comando Reduce." }], "Subsection", CellChangeTimes->{{3.4276522377444563`*^9, 3.4276522942110643`*^9}, { 3.427652325314879*^9, 3.427652484971346*^9}, {3.427652586383963*^9, 3.427652614749086*^9}, {3.427778304940464*^9, 3.4277783057665443`*^9}, 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StyleBox[GridBox[{ { RowBox[{ RowBox[{ RowBox[{"2", "x"}], "+", RowBox[{"3", "y"}]}], "=", "4"}]}, { RowBox[{ RowBox[{ RowBox[{ RowBox[{"3", "x"}], "-", RowBox[{"4", "y"}]}], "\[LessEqual]", "5"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"x", "-", RowBox[{"2", "y"}]}], ">", RowBox[{"-", "21"}]}]}]} }], 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}, {3.4276964538491907`*^9, 3.427696494513392*^9}, {3.4276965363151617`*^9, 3.42769653741392*^9}, { 3.427696585014299*^9, 3.427696587567273*^9}, {3.427778410496237*^9, 3.427778411298833*^9}, 3.4644350281083765`*^9}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.42866816446875*^9}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Ejercicio 11\nHallar los valores enteros de x e y que verifican:\n\ta) ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SuperscriptBox["x", "2"], "+", "xy", "+", SuperscriptBox["y", "2"]}], "=", "109"}], TraditionalForm]], "None"], "\n\tb) ", Cell[BoxData[ RowBox[{ RowBox[{ SuperscriptBox["x", "2"], "-", RowBox[{"6", "xy"}], "+", RowBox[{"9", SuperscriptBox["y", "2"]}], "-", "x", "+", RowBox[{"2", "y"}]}], "=", "1"}]], "None"], "\n\tc) ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SuperscriptBox["x", "3"], "-", RowBox[{"2", SuperscriptBox["x", "2"], "y"}], "+", SuperscriptBox["y", "3"]}], "=", "2"}], TraditionalForm]], "None"], "\n\td) ", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{"{", StyleBox[GridBox[{ { RowBox[{ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]}], "=", "1"}]}, { RowBox[{ RowBox[{ SuperscriptBox["x", "2"], "-", "y"}], "=", "2"}]} }], ShowAutoStyles->True]}], ShowAutoStyles->False], TraditionalForm]]] }], "Subsection", CellChangeTimes->{{3.4276967262654743`*^9, 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