Question 167
Prove that for all positive real numbers $a, b, c$ we have
$$
a+\sqrt{a b}+\sqrt[3]{a b c} \leq \frac{4}{3}(a+b+c)
$$
$$
a+\sqrt{a b}+\sqrt[3]{a b c} \leq \frac{4}{3}(a+b+c)
$$
MathNet 2016-part-02 — 184 problems (EN–VI) Question 167
Math Olympiad Vault · MathNet 2016-part-02 — 184 problems (EN–VI)