You'd have to prove the cauchy-shwartz thm wouldn't you?
I don't see how
a^2 + b^2 + c^2 >= |ab + bc + ac|
It's a well-known theorem, so i don't suppose you would have to prove it. However, if it makes you feel better, you shouldn't have much trouble finding a proof on the internet, or maybe TPH would like to give you one