Question

Find two positive numbers whose sum is 16 and the sum of whose squares is minimum.

Answer 1

Consider the number as x and 16 – x

We know that

S = x² + (16 – x)²

It can be written as

S = x² + 256 – 32x + x² = 2x² – 32x + 256

By differentiating w.r.t. x

Here x = 8 is the point of minimum and 8, 8 are the required numbers.