Question 104
For positive numbers $x$, $y$, $z$ prove inequality:
$$
\frac{1}{3}(x^3 + y^3 + z^3) \geq xyz + \frac{2}{9}(x + y + z)(x - z)^2 .
$$
$$
\frac{1}{3}(x^3 + y^3 + z^3) \geq xyz + \frac{2}{9}(x + y + z)(x - z)^2 .
$$
MathNet 2018-part-06 — 181 problems (EN–VI) Question 104
Math Olympiad Vault · MathNet 2018-part-06 — 181 problems (EN–VI)