Is this correct method to prove that $a^2 + b^2 + c^2 ≥ ab + bc + ac$, when $a,b,c \geq 0$? Can I prove it like this: Let's say that $a=b=c$ so we get "If $a \geq 0$ then $3a^2 ≥ 3a^2$" Now I take the negation of that statement and get "If $a \geq 0$ then $3a^2 < 3a^2$" The anti-thesis is obviously wrong which makes the original thesis right? Is this a correct way to do this, if not can you give some tips for what to do. I am not looking for complete solution as these are my homework and I really need to practice. 

Hint: Notice that $(a-b)^2 \geq 0.$ What happens when you sum three different such  inequalities: $(a-b)^2 \geq 0$, $(b-c)^2 \geq 0$, $(a-c)^2 \geq 0$?
