Question 63
For all non-negative real numbers $x$, $y$, $z$ with $x \ge y$, prove the inequality
$$
\frac{x^3 - y^3 + z^3 + 1}{6} \ge (x - y) \sqrt{xyz}.
$$
$$
\frac{x^3 - y^3 + z^3 + 1}{6} \ge (x - y) \sqrt{xyz}.
$$
MathNet 2019-part-01 — 184 problems (EN–VI) Question 63
Math Olympiad Vault · MathNet 2019-part-01 — 184 problems (EN–VI)