prove that $a^2+b^2+c^2 \geq a+b+c$ Let $a,b,c$ are positive real numbers such that $abc=1,$
prove that $$a^2+b^2+c^2 \geq a+b+c$$
i was thinking of using AM GM  inequlaity.but donot have idea on which pairs to apply it. 
any hint....

By QM-AM for the first inequality and AM-GM for the second,
$$\frac{a^2+b^2+c^2}{3}\geq\left( \frac{a+b+c}{3} \right)^2\geq\frac{a+b+c}{3}\left( \sqrt[3]{abc} \right)$$
so since $abc=1, a^2+b^2+c^2\geq a+b+c$
