How to prove $a^2 + b^2 + c^2 \ge ab + bc + ca$? How can the following inequation be proven?
$$a^2 + b^2 + c^2 \ge ab + bc + ca$$

for $a,b,c>=0$
we know $(a-b-c)^2>=0$ 
i.e $a^2 + b^2 + c^2 - 2 (ab + bc + ca) \ge 0$
i.e $a^2 + b^2 + c^2 \ge ab + bc + ca$
