Question 18
Let $a$, $b$, $c$ be positive real numbers such that $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = a + b + c$. Prove that
$$
\frac{1}{(2a + b + c)^2} + \frac{1}{(2b + c + a)^2} + \frac{1}{(2c + a + b)^2} \leq \frac{3}{16}
$$
$$
\frac{1}{(2a + b + c)^2} + \frac{1}{(2b + c + a)^2} + \frac{1}{(2c + a + b)^2} \leq \frac{3}{16}
$$