document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=909164>Question 909164</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two numbers such that their sum multiplied by the sum of their squares is 65, and the difference multiplied by the difference of their square is 5. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #551659 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=551659\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x+y)(x^2+y^2)=65\r<BR>\n" );
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document.write( "x(x^2+y^2)+y(x^2+y^2)=65\r<BR>\n" );
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document.write( "x^3+xy^2+x^2y+y^3=65..................(1)\r<BR>\n" );
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document.write( "(x-y)(x^2-y^2)=5\r<BR>\n" );
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document.write( "x(x^2-y^2)-y(x^2-y^2)=5\r<BR>\n" );
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document.write( "x^3-xy^2-x^2y+y^3=5.....................(2)\r<BR>\n" );
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document.write( "add (1) & (2)\r<BR>\n" );
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document.write( "2x^3+2y^3=70\r<BR>\n" );
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document.write( "x^3+y^3=35.........................(3)\r<BR>\n" );
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document.write( "subtract (2) from (1)\r<BR>\n" );
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document.write( "2x^2y+2xy^2=60<BR>\n" );
document.write( "2xy(x+y)=60<BR>\n" );
document.write( "xy(x+y)=30\r<BR>\n" );
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document.write( "from (3)<BR>\n" );
document.write( "x^3+y^3=35.........................(3)\r<BR>\n" );
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document.write( "(x+y)^3-3xy(x+y)=35\r<BR>\n" );
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document.write( "(x+y)^3+3(30)=35\r<BR>\n" );
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document.write( "(x+y)^3=90+35\r<BR>\n" );
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document.write( "(x+y)^3=125<BR>\n" );
document.write( "(x+y)=5...........................(4)\r<BR>\n" );
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document.write( "Now we know<BR>\n" );
document.write( "(x-y)(x^2-y^2)=5\r<BR>\n" );
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document.write( "(x-y)(x+y)(x-y)=5<BR>\n" );
document.write( "(x+y)(x-y)^2=5\r<BR>\n" );
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document.write( "5(x-y)^2=5\r<BR>\n" );
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document.write( "(x-y)^2=5/5=1\r<BR>\n" );
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document.write( "x-y=+/-1...................................(5)\r<BR>\n" );
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document.write( "solve (4)&(5) \r<BR>\n" );
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document.write( "we have (2,3) OR (3,2) as the solutions\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );