Question 157
Let $a$, $b$ and $c$ be positive real numbers such that $a + b + c = 3$. Prove that
$$
\frac{a + b}{2ab + 1} + \frac{b + c}{2bc + 1} + \frac{c + a}{2ca + 1} \ge 2.
$$
$$
\frac{a + b}{2ab + 1} + \frac{b + c}{2bc + 1} + \frac{c + a}{2ca + 1} \ge 2.
$$