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`.
`:. 4x-30 = 0`
`=> x = 7.5`
So, the numbers are `7.5 and 7.5`