Find three numbers whose sum is 6 and whose sum of squares is a minimum. Can someone help me set this up?

Question

bahrom7893 · Answer

x+y+z=6
x^2+y^2+z^2 is a minimum.

bahrom7893 · Answer

hmm u sure this is algebra 2?

anonymous · Answer

I said above algebra ;)

bahrom7893 · Answer

oh u just gotta set this up.

anonymous · Answer

I have to solve using partials, but I just can't get it set up right

bahrom7893 · Answer

u learn partial derivatives in algebra?

anonymous · Answer

I'm in calc III

bahrom7893 · Answer

lol sorry man, look up lagrange multipliers, I totally forgot my calc 3. @Zarkon  can u help this guy out?

anonymous · Answer

thanks anyway :)

zarkon · Answer

yes...this problem is trivial with lagrange multipliers

zarkon · Answer

just compute $$\nabla(x^2+y^2+z^2)=\lambda \nabla(x+y+z-6)$$

anonymous · Answer

i got it. it is 2,2,2 i was not expanding my z. thanks guys!

zarkon · Answer

that's it.  though I'm not sure what you mean about expanding your z

$$2x=\lambda$$
$$2y=\lambda$$
$$2z=\lambda$$

$$\Rightarrow x=y=z$$

$$x+y+z=6\Rightarrow x+x+x=6\Rightarrow x=2\Rightarrow y=2\Rightarrow z=2$$