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

In summary, the question asks to find three positive numbers that sum up to 12 and have the smallest possible sum of squares. This can be solved by using the equation f(x,y,z) = x^2 + y^2 + z^2 and the fact that x+y+z=12, which can be used to reduce the problem to 2D.
  • #1
ScienceGeek24
164
0

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!
 
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  • #2
Hi ScienceGeek24! :smile:

Start by calling the three numbers x y and z, and putting f(x,y,z) = x2 + y2 + z2 :wink:
 
  • #3
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.
 

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