Question

Please explain how to do it as well as result:
The sum of two non-negative numbers is 20. Find the numbers If the sum of their squares is as large as possible; as small as possible. This is optimization.

Answer 1

if the sum is \(20\) and one is say \(x\) then the other is \(20-x\) maximize
\[f(x)=x^2+(20-x)^2\]

Answer 2

not sure what you are supposed to use, but
\[f(x)=2 x^2-40 x+400\] is a quadratic, min is at the vertex