UA-UMO 2005 Problem 106

If $a,b,c$ are positive real numbers, prove the inequality:

$\frac {a^2}{b} + \frac {b^3}{c^2} + \frac {c^4}{a^3} \ge - a + 2b + 2c.$

P.S. Thank you for the observation. I've already corrected it.