Prove that $a+b+c\le \frac {a^3}{bc} + \frac {b^3}{ac} + \frac {c^3}{ab}$ One of my friend had just given me an inequality to solve which is stated below. 
Consider the three positive reals $a, b, c$ then prove that 

$$a+b+c\le \frac {a^3}{bc} + \frac {b^3}{ac} + \frac {c^3}{ab}$$

I have solved this inequality very easily using Muirhead. But my friend has no idea what Muirhead inequality is. So I want to know whether there is any other method to solve this problem except for Muirhead's inequality.

This is the same as
$$a^4+b^4+c^4\ge abc(a+b+c).$$
By AM/GM,
$$2a^4+b^4+c^4\ge 4a^2bc.$$
Now add the cyclic permutations of this.
