math
posted by Anonymous on .
Find two positive numbers whose sum is 50 such that the sum of their squares is minimum?

let one number be x
then the other is 50x
let the sum of their squares be S
S = x^2 + (50x)^2
= 2x^2  100x + 2500
dS/dx = 4x  100
= 0 for a min of S
4x100 = 0
x = 25
The numbers are 25 and 25