Miscelánea2 de álgebra

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=77 BGCOLOR="#009999" TEXT="#080000" bgproperties="fixed" background="045005c0ermwos.gif"> <div> <A HREF="id424.htm" TARGET="_top" TITLE="Misceláneas"><U><B>Misceláneas </B></U></A><B> | </B><A HREF="index.htm" TARGET="_top" TITLE="Á l g e b r a d e B a l d o r"><U><B>Página principal</B></U></A><B> |  </B><A HREF="index.htm" TARGET="_top" TITLE="Á l g e b r a d e B a l d o r"><U><B> Álgebra de Baldor</B></U></A><B>    | </B><B> </B><B> </B><B>  </B><FONT SIZE="5" COLOR="#00FFCC" FACE="Arial" ><B>Precálculo21</B></FONT></div> <div> <A HREF="id376.htm" TARGET="_top" TITLE="Miscelánea1 de álgebra"><U><B>Miscelánea1 de álgebra</B></U></A><B>   |   </B><B>Miscelánea2  de álgebra</B><B>   |   </B><A HREF="id406.htm" TARGET="_top" TITLE="Miscelánea3Álgebra"><U><B>Miscelánea3-Álgebra</B></U></A><B>   |   </B><A HREF="id408.htm" TARGET="_top" 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BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="647" BORDERCOLORLIGHT="#33FFCC" BORDERCOLORDARK="#009900" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP COLSPAN=3 BGCOLOR=#00CC99 HEIGHT= 20 WIDTH="635"><div> <B> <A NAME="e_j_e_r_c_i_c_i__o_s"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>E j e r c i c i  o s</B></div> </tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 71 ><NOBR><div> <A HREF="#1" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="7bd3f400.gif" border=0 width="319" height="64" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="305"><div> <A HREF="#2" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="7e5a92f0.gif" border=0 width="169" height="47" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 131 ><NOBR><div> <A HREF="#3" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="7e924370.gif" border=0 width="292" height="55" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="305"><div> <A HREF="#4" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="85b8c7c0.gif" border=0 width="140" height="124" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=3 HEIGHT= 60 ><NOBR><div> <A HREF="#5" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="88b5d350.gif" border=0 width="605" height="53" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 108 ><NOBR><div> <A HREF="#6" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="8d31f180.gif" border=0 width="287" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#7" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="8f714650.gif" border=0 width="276" height="101" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=3 HEIGHT= 108 ><NOBR><div> <A HREF="#8" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="90d53650.gif" border=0 width="595" height="101" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 52 ><NOBR><div> <A HREF="#9" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="915e32d0.gif" border=0 width="227" height="45" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#10" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="9c9112d0.gif" border=0 width="273" height="45" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=3 HEIGHT= 44 ><NOBR><div> <A HREF="#11" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="9cb6b250.gif" border=0 width="619" height="37" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 60 ><NOBR><div> <A HREF="#12" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="a1fb5290.gif" border=0 width="181" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP COLSPAN=2><NOBR><div> <A HREF="#13" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="a5198350.gif" border=0 width="408" height="53" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=3 HEIGHT= 76 ><NOBR><div> <A HREF="#14" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="a5747450.gif" border=0 width="583" height="69" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 58 ><NOBR><div> <A HREF="#15" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="b363c280.gif" border=0 width="316" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#16" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="b39d7330.gif" border=0 width="215" height="51" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 79 ><NOBR><div> <A HREF="#17" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="b3d9f300.gif" border=0 width="159" height="48" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP COLSPAN=2 WIDTH="434"><div> <A HREF="#18" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="b4005480.gif" border=0 width="261" height="72" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 44 ><NOBR><div> <A HREF="#19" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="b43b01b0.gif" border=0 width="176" height="27" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP COLSPAN=2><NOBR><div> <A HREF="#20_" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="cdbb4250.gif" border=0 width="436" height="37" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=3 HEIGHT= 74 ><NOBR><div> <A HREF="#21_" TITLE="Miscelánea2 de álgebra"><U><IMG SRC="ce16d430.gif" border=0 width="621" height="67" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> </TABLE></div> <bR> <div> <B>S o l u c i o n e s</B></div> <bR> <div> <B> <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="7be5b170.gif" border=0 width="91" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="7c5a4d70.gif" border=0 width="676" height="471" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="7e65b170.gif" border=0 width="91" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="7e8abc50.gif" border=0 width="683" height="197" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="7ea5b170.gif" border=0 width="91" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="7ebefd70.gif" border=0 width="751" height="471" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <bR> <div> <B> <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="85c5b170.gif" border=0 width="91" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="85e54a00.gif" border=0 width="596" height="416" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="88a5b170.gif" border=0 width="91" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="88d8dc40.gif" border=0 width="653" height="1220" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="8d45b170.gif" border=0 width="91" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="8d7791d0.gif" border=0 width="633" height="285" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="8f85b170.gif" border=0 width="91" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="8fb78a50.gif" border=0 width="632" height="677" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="92b5b170.gif" border=0 width="91" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="931c1d30.gif" border=0 width="705" height="979" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="9"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="9165b170.gif" border=0 width="91" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="9171d190.gif" border=0 width="541" height="281" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="10"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="95a5b170.gif" border=0 width="91" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="9cadba70.gif" border=0 width="475" height="167" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="11"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="9cc5b170.gif" border=0 width="91" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="9cd2b770.gif" border=0 width="555" height="119" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="12"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="a2063170.gif" border=0 width="99" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="a21cce00.gif" border=0 width="460" height="224" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="13"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="a5363170.gif" border=0 width="99" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="a541bab0.gif" border=0 width="539" height="683" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="14"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="a5563170.gif" border=0 width="99" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="a58b7c50.gif" border=0 width="439" height="197" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="15"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="b3763170.gif" border=0 width="99" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="b3887e00.gif" border=0 width="647" height="224" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="16"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="b3a63170.gif" border=0 width="99" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="b3c6b7d0.gif" border=0 width="619" height="125" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="17"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="b3f63170.gif" border=0 width="99" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="b3e5d4b0.gif" border=0 width="605" height="75" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="18"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="b4163170.gif" border=0 width="99" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="b4239f30.gif" border=0 width="569" height="243" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="19"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="b4463170.gif" border=0 width="99" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="b454c900.gif" border=0 width="588" height="144" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="20_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>20.  </B><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" ><U>Solución</U>:</FONT></div> <div> <IMG SRC="cdd5c350.gif" border=0 width="604" height="309" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <B> <A NAME="21_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>21.  </B><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" ><U>Solución</U>:</FONT></div> <div> <IMG SRC="ce691e00.gif" border=0 width="657" height="992" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <bR> <bR> <bR> </td> </tr><tr> <td valign="top" colspan=2 height=14 BGCOLOR="#009999" TEXT="#080000"> <bR> </td> </tr></table></body>