IN-TST 2002 Problem 5

Let $a,b,c$ be positive reals such that $a^2+b^2+c^2=3abc$ . Prove that $$\frac{a}{b^2c^2}+\frac{b}{c^2a^2}+\frac{c}{a^2b^2} \geq \frac{9}{a+b+c}$$