Question 40
Let $a$, $b$, $c$ be positive real numbers such that $abc = 1$. Prove that
$$
\frac{1}{a^5+b^5+c^2} + \frac{1}{b^5+c^5+a^2} + \frac{1}{c^5+a^5+b^2} \le 1
$$
$$
\frac{1}{a^5+b^5+c^2} + \frac{1}{b^5+c^5+a^2} + \frac{1}{c^5+a^5+b^2} \le 1
$$