Question 78
If $a, b, c \in \mathbb{R}^+$ such that $(a+b)(b+c)(c+a)=8$, then prove that
$$
\frac{a+b+c}{3} \geq \sqrt[27]{\frac{a^3+b^3+c^3}{3}}.
$$
$$
\frac{a+b+c}{3} \geq \sqrt[27]{\frac{a^3+b^3+c^3}{3}}.
$$
MathNet 2008-part-03 — 165 problems (EN–VI) Question 78
Math Olympiad Vault · MathNet 2008-part-03 — 165 problems (EN–VI)