JBMO-SL 2002 Problem 5

Let $a,b,c$ be positive real numbers. Prove the inequality: $\frac {a^3}{b^2} + \frac {b^3}{c^2} + \frac {c^3}{a^2}\ge \frac {a^2}{b} + \frac {b^2}{c} + \frac {c^2}{a}$