What is the smallest possible value of the sum of their squares if the sum of two positive numbers is 16?

1 Answer
Alan P.
Feb 16, 2015

If the sum of two positive integers, x and y is 16
x + y = 16
y = (16 - x)

The sum of their squares is
x^2 + (16 - x)^2
=2x^2 -32x +256

The minimum will occur when the derivative = 0
i.e. when 4x - 32 = 0
That is the minimum occurs at (x,y) = (8,8)
and the minimum possible value of the sum of the squares is
8^2 + 8^2
=128

Related questions
See all questions in Solving Optimization Problems
Impact of this question
44668 views around the world
You can reuse this answer
Creative Commons License