Question 181
Let $a$, $b$, $x$, $y$, $z$ be positive real numbers. Prove the inequality
$$
\frac{x}{a y+b z}+\frac{y}{a z+b x}+\frac{z}{a x+b y} \geq \frac{3}{a+b} .
$$
$$
\frac{x}{a y+b z}+\frac{y}{a z+b x}+\frac{z}{a x+b y} \geq \frac{3}{a+b} .
$$
MathNet 2018-part-06 — 181 problems (EN–VI) Question 181
Math Olympiad Vault · MathNet 2018-part-06 — 181 problems (EN–VI)