document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1020225>Question 1020225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x and y are real, x^4y^5+x^5y^4 = 810 & x^6y^3+x^3y^6 = 945, Find 2x^3+(xy)^3+2y^3 = ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #636162 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=636162\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4y%5E5%2Bx%5E5y%5E4+=+810+ ALIGN=MIDDLE  ALT=\"x%5E4y%5E5%2Bx%5E5y%5E4+=+810+\"   DISABLED_style= \"max-width:90%; height:auto;\" >==><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3y%5E3%28x%5E2y%2Bxy%5E2%29+=+810 ALIGN=MIDDLE  ALT=\"x%5E3y%5E3%28x%5E2y%2Bxy%5E2%29+=+810\"   DISABLED_style= \"max-width:90%; height:auto;\" > after factoring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3y%5E3 ALIGN=MIDDLE  ALT=\"x%5E3y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and changing the order of the terms.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3y%5E3%283x%5E2y%2B3xy%5E2%29+=+2430 ALIGN=MIDDLE  ALT=\"x%5E3y%5E3%283x%5E2y%2B3xy%5E2%29+=+2430\"   DISABLED_style= \"max-width:90%; height:auto;\" >     (Equation A)\r<BR>\n" );
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document.write( "after multiplying both sides by 3.\r<BR>\n" );
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document.write( "Similarly, factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3y%5E3 ALIGN=MIDDLE  ALT=\"x%5E3y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the 2nd equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6y%5E3%2Bx%5E3y%5E6+=+945 ALIGN=MIDDLE  ALT=\"x%5E6y%5E3%2Bx%5E3y%5E6+=+945\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3y%5E3%28x%5E3+%2B+y%5E3%29+=+945 ALIGN=MIDDLE  ALT=\"x%5E3y%5E3%28x%5E3+%2B+y%5E3%29+=+945\"   DISABLED_style= \"max-width:90%; height:auto;\" >             (Equation B)\r<BR>\n" );
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document.write( "Add corresponding sides of Eqn. A and Eqn. B, to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3y%5E3%28x%5E3+%2B+3x%5E2y%2B3xy%5E2%2B+y%5E3%29+=+3375 ALIGN=MIDDLE  ALT=\"x%5E3y%5E3%28x%5E3+%2B+3x%5E2y%2B3xy%5E2%2B+y%5E3%29+=+3375\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "==><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3y%5E3%28x%2By%29%5E3+=+3375 ALIGN=MIDDLE  ALT=\"x%5E3y%5E3%28x%2By%29%5E3+=+3375\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> xy(x+y) = 15,                         (Equation C)<BR>\n" );
document.write( "after taking cube roots of both sides.\r<BR>\n" );
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document.write( "Now the first equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4y%5E5%2Bx%5E5y%5E4+=+810+ ALIGN=MIDDLE  ALT=\"x%5E4y%5E5%2Bx%5E5y%5E4+=+810+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4y%5E4%28x%2By%29+=+810 ALIGN=MIDDLE  ALT=\"x%5E4y%5E4%28x%2By%29+=+810\"   DISABLED_style= \"max-width:90%; height:auto;\" >                 (Equation D)<BR>\n" );
document.write( "Dividing Eqn.D by Eqn.C, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3y%5E3+=+810%2F15+=54 ALIGN=MIDDLE  ALT=\"x%5E3y%5E3+=+810%2F15+=54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28xy%29%5E3=54 ALIGN=MIDDLE  ALT=\"+%28xy%29%5E3=54\"   DISABLED_style= \"max-width:90%; height:auto;\" >               (Equation E)   \r<BR>\n" );
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document.write( "Putting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3y%5E3+=+54 ALIGN=MIDDLE  ALT=\"x%5E3y%5E3+=+54\"   DISABLED_style= \"max-width:90%; height:auto;\" > into Eqn.B, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54%28x%5E3%2By%5E3%29+=+945 ALIGN=MIDDLE  ALT=\"54%28x%5E3%2By%5E3%29+=+945\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2By%5E3+=+35%2F2 ALIGN=MIDDLE  ALT=\"x%5E3%2By%5E3+=+35%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3%2B2y%5E3+=+35 ALIGN=MIDDLE  ALT=\"2x%5E3%2B2y%5E3+=+35\"   DISABLED_style= \"max-width:90%; height:auto;\" >                    (Equation F)\r<BR>\n" );
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document.write( "Finally, combining Equations E and F, we get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3%2B%28xy%29%5E3%2B2y%5E3+=+35%2B54+=+highlight%2889%29 ALIGN=MIDDLE  ALT=\"2x%5E3%2B%28xy%29%5E3%2B2y%5E3+=+35%2B54+=+highlight%2889%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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