Question 8
Let $x, y, z$ be positive real numbers. Prove that
$$
\sum_{cyclic} \frac{xy}{xy + x^2 + y^2} \le \sum_{cyclic} \frac{x}{2x + z}.
$$
$$
\sum_{cyclic} \frac{xy}{xy + x^2 + y^2} \le \sum_{cyclic} \frac{x}{2x + z}.
$$
MathNet 2009-part-02 — 175 problems (EN–VI) Question 8
Math Olympiad Vault · MathNet 2009-part-02 — 175 problems (EN–VI)