MathNet 2008-part-04 — 165 problems (EN–VI) Question 131

Prove the inequality $\frac{a^2}{bc(a^2+b^2)} + \frac{b^2}{ca(b^2+c^2)} + \frac{c^2}{ab(c^2+a^2)} \ge \frac{9}{2}$ for arbitrary positive numbers $a, b, c$ satisfying $ab + bc + ca = 1$.