Question 129
Let $x$, $y$, $z$ be positive real numbers. Prove that
$$
\frac{(x+y)(x+z)(y+z)}{4 x y z} \geq \frac{x+z}{y+z}+\frac{y+z}{x+z}
$$
$$
\frac{(x+y)(x+z)(y+z)}{4 x y z} \geq \frac{x+z}{y+z}+\frac{y+z}{x+z}
$$
MathNet 2023-part-03 — 191 problems (EN–VI) Question 129
Math Olympiad Vault · MathNet 2023-part-03 — 191 problems (EN–VI)