document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964446>Question 964446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of two numbers is 640. Their difference is 12. Find these numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589344 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=589344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let's call the numbers a and b:<BR>\n" );
document.write( "ab= 640<BR>\n" );
document.write( "a-b= 12 and therefore a= 12+b Substitute in the first equation:<BR>\n" );
document.write( "b(12+b)= 640<BR>\n" );
document.write( "12b+b^2= 640 We now have a quadratic binomial:<BR>\n" );
document.write( "b^2+12b-640= 0 factor the equation<BR>\n" );
document.write( "(b+32)(b-20)= 0 Now solve each separately:<BR>\n" );
document.write( "b+32= 0 or b-20= 0<BR>\n" );
document.write( "b= -32 or b= 20 We toss out the negative and keep the 20<BR>\n" );
document.write( "So, one number is 20 and the other is 640/20= 32.<BR>\n" );
document.write( "Proof: <BR>\n" );
document.write( "32*20= 640 and<BR>\n" );
document.write( "32-20 = 12 </SPAN>\n" );
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