prove that $\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}\geq a+b+c$ 
If $a,b,c>0$, Then prove that $$\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}\geq a+b+c$$

$\bf{My\; Try::}$ Using Cauchy- Schwarz Inequality
$$\frac{a^4}{abc}+\frac{b^4}{abc}+\frac{c^4}{abc}\geq \frac{a^2+b^2+c^2}{3abc}$$
Now How can i solve after that , Help required, Thanks 

You can actually use Holder's inequality for three variables in the following way:
$$(b+c+a)(c+a+b) \Big(\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}\Big) \geqslant (a+b+c)^3 $$
From where you get:
$$ \frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab} \geqslant a+b+c$$
