How to Minimize the Sum of Squares of Three Numbers That Add Up to 12?

[ScienceGeek24]

Homework Statement

Find three positive numbers whose sum is 12 and the sum of whose squares is as small as possible.

Homework Equations

The Attempt at a Solution

I don;t even know how to start this one, this is a section from partial derivatives on the max and mins. Please i need guidance through this exercise. Thank you!

 

[tiny-tim]

Hi ScienceGeek24!

Start by calling the three numbers x y and z, and putting f(x,y,z) = x² + y² + z²

 

[skiller]

In addition to tiny-tim's good first idea, how about using the fact that you know that x+y+z=12, so you know what z is in terms of x and y - then you only have a 2D problem to solve.