document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=495198>Question 495198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is 24.Find the two numbers if their product is to be a maximum. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #336008 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=336008\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a and b are the numbers with a+b = 24, AM-GM inequality states that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{a+b}{2} \ge \sqrt{ab}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 12 \ge \sqrt{ab} \Rightarrow 144 \ge ab\">\r<BR>\n" );
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document.write( "Equality occurs when a = b = 12, so the numbers are 12 and 12.\r<BR>\n" );
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document.write( "Note that we could do it using calculus or finding the vertex of a quadratic equation, but this solution is a little more slick. </SPAN>\n" );
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