Find two positive numbers whose sum is 50 such that the sum of their squares is minimum?

Answer 1

let one number be x
then the other is 50-x

let the sum of their squares be S
S = x^2 + (50-x)^2
= 2x^2 - 100x + 2500
dS/dx = 4x - 100
= 0 for a min of S
4x-100 = 0
x = 25

The numbers are 25 and 25