Question 53
The positive real numbers $a$, $b$, $c$ satisfy the relation $a^{2} + b^{2} + c^{2} = 3 a b c$. Prove the inequality
$$
\frac{a}{b^{2} c^{2}} + \frac{b}{c^{2} a^{2}} + \frac{c}{a^{2} b^{2}} \geq \frac{9}{a + b + c}
$$
$$
\frac{a}{b^{2} c^{2}} + \frac{b}{c^{2} a^{2}} + \frac{c}{a^{2} b^{2}} \geq \frac{9}{a + b + c}
$$