Proof help: Prove that $x^2+y^2+z^2 \geq xy+xz+yz$ $x^2+y^2+z^2 \geq xy+xz+yz $ for all real numbers, x, y, and z.
I'm not very good with working inequality proofs. Can someone help me prove this? The technique doesn't really matter.

First observe that $ (x-y)^2 + (x-z)^2 + (y-z)^2 \geq 0 $.
Next, expand the LHS to obtain:
$ 2x^2 + 2y^2 + 2z^2 - 2xy - 2xz - 2yz \geq 0 $
Now you simply divide by two and add $xy + xz + yz$ to both sides.
