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

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 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