document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=140974>Question 140974</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find x^2 + y^2 if x and y are positive integers such that:\r<BR>\n" );
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document.write( "xy + x + y = 71<BR>\n" );
document.write( "x^2y + xy^2 = 880 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #102906 by </B><A HREF=/tutors/aboutme.mpl?userid=oscargut><B>oscargut(2103)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oscargut><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=oscargut><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=102906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> xy + x + y = 71<BR>\n" );
document.write( "x^2y + xy^2 = 880\r<BR>\n" );
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document.write( "using 2nd eq then xy(x+y)=880<BR>\n" );
document.write( "then using 1st eq xy(71-xy)=880\r<BR>\n" );
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document.write( "let w=xy then  -w^2+71w-880=0\r<BR>\n" );
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document.write( "xy=16 or xy=55<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x+y=55 or x+y=16\r<BR>\n" );
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document.write( "case 1)xy=16 and x+y=55 (is not possible) because x and y positive integers<BR>\n" );
document.write( "case 2)xy=55 and x+y=16 (x=11,y=5 or x=5,y=11)<BR>\n" );
document.write( "x^2+y^2= (x+y)^2-2xy = 16^2-2(55)=146\r<BR>\n" );
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document.write( "Answer: x^2+y^2=146\r<BR>\n" );
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document.write( " </SPAN>\n" );
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