document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=45868>Question 45868</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi again,\r<BR>\n" );
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document.write( "I could use some assistance with this problem:\r<BR>\n" );
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document.write( "Prove that if the sum of two numbers is constant, then their product is maximum if the numbers are equal. \r<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Louis </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #30451 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=30451\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Prove that if the sum of two numbers is constant, then their product is maximum if the numbers are equal. \r<BR>\n" );
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document.write( "1st: Let x+y = k, where k is some constant.<BR>\n" );
document.write( "2nd: Then y=k-x<BR>\n" );
document.write( "3rd: The product of x and y is xy=x(k-x)=kx-x^2<BR>\n" );
document.write( "This is a quadratic with a=-1, b=k<BR>\n" );
document.write( "The maximum value of this product occurs when x=-b/2a<BR>\n" );
document.write( "x=-b/2a= -k/-2 = k/2<BR>\n" );
document.write( "Substitute that into the 1st equation to get the following:<BR>\n" );
document.write( "(k/2)+ y=k<BR>\n" );
document.write( "y=k/2<BR>\n" );
document.write( "So both x and y are k/2; therefore they are equal.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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