Question

The sum of two nonnegative numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible.

Answer 1

x+y=20
A=x^2+y^2
A=x^2+(20-x)^2
A=2x^2-40x+400
A'=4x-40=0
x=10
y=10

Answer 2

10^2+10^2=200 is min.

20^2+0^=400 max