Inequality. $a^2+b^2+c^2 \geq a+b+c$ Let $a,b,c$ be positive real numbers such that $abc=1$. Prove that 
$a^2+b^2+c^2 \geq a+b+c$. 
Thanks

Since $(2,0,0)\succ\left(\frac{4}{3},\frac{1}{3},\frac{1}{3}\right)$, by Murhead we obtain:
 $$a^2+b^2+c^2\geq\sum_{cyc}a^{\frac{a}{3}}b^{\frac{1}{3}}c^{\frac{1}{3}}=a+b+c$$
