Question

The sum of two numbers is 20. What is the least possible sum of their squares?

Answer 1

`200`

Explanation:

`x + y = 20`

`f(x,y) = x^2 + y^2`

`y = 20 - x`

`S(x) = x^2 + (20 - x)^2 = 2x^2 - 40x + 400`

We want the vertex.

`x_V = -b/(2a) = 40/4 = 10`

`S(10) = 10^2 + 10^2 = 200`