Question 117
For positive numbers $a$, $b$, $c$, such that $abc = 1$, prove the inequality:
$$
\frac{a^2 + b^2}{c^2 + a + b} + \frac{b^2 + c^2}{a^2 + b + c} + \frac{c^2 + a^2}{b^2 + c + a} \le 2.
$$
$$
\frac{a^2 + b^2}{c^2 + a + b} + \frac{b^2 + c^2}{a^2 + b + c} + \frac{c^2 + a^2}{b^2 + c + a} \le 2.
$$