document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=366968>Question 366968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two positive numbers that satisfy the given requirements:  the sum of the first number squared and the second is 54 and the product is 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 #261593 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=261593\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find two positive numbers that satisfy the given requirements: the sum of the first number squared and the second is 54 and the product is a maximum.<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "1st: x<BR>\n" );
document.write( "2nd: y<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "x^2+y = 54<BR>\n" );
document.write( "y = 54-x^2<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Product = x(54-x)^2 = 54x-x^3<BR>\n" );
document.write( "----<BR>\n" );
document.write( "dP/dx = 54-3x^2<BR>\n" );
document.write( "Solve: 54-3x^2 = 0<BR>\n" );
document.write( "3x^2=54<BR>\n" );
document.write( "x^2 = 18<BR>\n" );
document.write( "x = sqrt(18)<BR>\n" );
document.write( "y = 54-(sqrt(18))^2 = 36<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "-------- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );