Determine two positive numbers whose sum is 15 and the sum of whose squares is minimum.

Explanation

Let the two positive numbers are `x` and `15-x`.

Let `y` is the sum of their squares.


Now, `y = x^2+(15-x)^2`

`=> y = x^2+225+x^2-30x`

`=>y = 2x^2-30x+225`

`=>dy/dx = 4x-30`

For, `y` to be minimum ,` dy/dx` should be `0`.

...