Question 120
Let $x$, $y$, $z \gt 0$. Prove that
$$
\frac{x^3}{z^3 + x^2 y} + \frac{y^3}{x^3 + y^2 z} + \frac{z^3}{y^3 + z^2 x} \ge \frac{3}{2}.
$$
$$
\frac{x^3}{z^3 + x^2 y} + \frac{y^3}{x^3 + y^2 z} + \frac{z^3}{y^3 + z^2 x} \ge \frac{3}{2}.
$$
MathNet 2015-part-04 — 191 problems (EN–VI) Question 120
Math Olympiad Vault · MathNet 2015-part-04 — 191 problems (EN–VI)