document.write( "Question 659966: Find two positive numbers whose product is 256 and whose sum is a minimum. List them in non-decreasing order.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #411001 by htmentor(1343) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find two positive numbers whose product is 256 and whose sum is a minimum. List them in non-decreasing order.
\n" ); document.write( "================================
\n" ); document.write( "Let x,y be the two integers
\n" ); document.write( "xy = 256 -> y = 256/x
\n" ); document.write( "The sum, S = x + y = x + 256/x
\n" ); document.write( "For S to be a minimum, dS/dx = 0:
\n" ); document.write( "0 = 1 - 256/x^2
\n" ); document.write( "x^2 - 256 = 0
\n" ); document.write( "(x+16)(x-16) = 0
\n" ); document.write( "Since the integers need to be positive, we have the solution x=16
\n" ); document.write( "If x=16, then y=16
\n" ); document.write( "Ans: 16 and 16 \n" ); document.write( "

\n" );