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Find two positive numbers whose product is 256 and whose sum is a minimum. List them in non-decreasing order.
Let x,y be the two integers
xy = 256 -> y = 256/x
The sum, S = x + y = x + 256/x
For S to be a minimum, dS/dx = 0:
0 = 1 - 256/x^2
x^2 - 256 = 0
(x+16)(x-16) = 0
Since the integers need to be positive, we have the solution x=16
If x=16, then y=16
Ans: 16 and 16