Question 25
Let $a, b, c$ be positive real numbers such that $ab + bc + ca = 1/3$. Prove the inequality
$$
\frac{a}{a^2 - bc + 1} + \frac{b}{b^2 - ca + 1} + \frac{c}{c^2 - ab + 1} \ge \frac{1}{a + b + c}
$$
$$
\frac{a}{a^2 - bc + 1} + \frac{b}{b^2 - ca + 1} + \frac{c}{c^2 - ab + 1} \ge \frac{1}{a + b + c}
$$