document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179956>Question 1179956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two numbers have a sum of 36.\r<BR>\n" );
document.write( "\n" );
document.write( "Write an equation for the product of the two numbers.\r<BR>\n" );
document.write( "\n" );
document.write( "Use roots to explain why the maximum product must occur when the<BR>\n" );
document.write( "two numbers are both 18. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #809545 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=809545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Given that the sum of the two numbers is 36, the solution from the other tutor uses the typical algebraic method, calling the numbers x and 36-x.<br><BR>\n" );
document.write( "Here is another approach....<br><BR>\n" );
document.write( "Let the two numbers be 18+x and 18-x; their sum is 36, as required.<br><BR>\n" );
document.write( "The product of the two numbers is then (18+x)(18-x)=324-x^2.<br><BR>\n" );
document.write( "In that form, the product is clearly a maximum when x=0, making the two numbers 18+0=18 and 18-0=18.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );