Question 20
Let $a$, $b$, $c$ be positive real numbers, with $abc(a + b + c) = 3$. Prove that
$$
\frac{1}{a^2 + b^2 + 1} + \frac{1}{b^2 + c^2 + 1} + \frac{1}{c^2 + a^2 + 1} \le 1.
$$
$$
\frac{1}{a^2 + b^2 + 1} + \frac{1}{b^2 + c^2 + 1} + \frac{1}{c^2 + a^2 + 1} \le 1.
$$