document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825600>Question 825600</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is 24.  The sum of the squares of the two numbers is 306.  What is the product of the two numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497437 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=497437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x + y = 24<BR>\n" );
document.write( "x^2 +y^2 = 306<BR>\n" );
document.write( "solve for x in the first equation<BR>\n" );
document.write( "(24-y)^2 +y^2 = 306<BR>\n" );
document.write( "576 -48y +y^2 +y^2 = 306<BR>\n" );
document.write( "2y^2 -48y +576 = 306<BR>\n" );
document.write( "divide both sides of = by 2<BR>\n" );
document.write( "y^2 -24y +288 = 153<BR>\n" );
document.write( "y^2 -24y +135 = 0<BR>\n" );
document.write( "factor this equation<BR>\n" );
document.write( "(y-15) * (y-9) = 0<BR>\n" );
document.write( "there are two solutions, (x=9, y=15) and (x=15,y-9)<BR>\n" );
document.write( "we are asked for the product of the two numbers<BR>\n" );
document.write( "9 * 15 = 15 * 9 = 135\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );