document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085089>Question 1085089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2 integers have a sum of 35. The sum of their squares is 637. Find the numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699123 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=699123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2 integers have a sum of 35. The sum of their squares is 637. Find the numbers.<BR>\n" );
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document.write( "35 = 5*7<BR>\n" );
document.write( "637 = 13*7^2<BR>\n" );
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document.write( "--> 2*7 & 3*7<BR>\n" );
document.write( "= 14 & 21<BR>\n" );
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document.write( "The long way:<BR>\n" );
document.write( "x + y = 35 --> y = 35-x<BR>\n" );
document.write( "x^2 + y^2 = 637<BR>\n" );
document.write( "Sub for y<BR>\n" );
document.write( "x^2 + (35-x)^2 = 637<BR>\n" );
document.write( "2x^2 - 70x + 1225 = 637<BR>\n" );
document.write( "2x^2 - 70x + 588 = 0<BR>\n" );
document.write( "x^2 - 35x + 294 = 0<BR>\n" );
document.write( "(x-14)*(x-21) = 0<BR>\n" );
document.write( "etc.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );