The sum of two nonnegative numbers is 100. What is the maximum value of the sum of the squares of these two numbers?

Question

The sum of two nonnegative numbers is 100. What is the maximum value of the sum of the squares of these two numbers?

Answer 1

x≥0, y≥0

x+y=100

max(x²+y²) =10000, is reached when x=0 and y=100 or x=100 and y=0.