Question 29
Let $a$, $b$, $c$, $d$ be nonnegative real numbers satisfying $a + b + c + d = 100$. Prove that
$$
\sqrt[3]{\frac{a}{b+7}} + \sqrt[3]{\frac{b}{c+7}} + \sqrt[3]{\frac{c}{d+7}} + \sqrt[3]{\frac{d}{a+7}} \le \frac{8}{\sqrt[3]{7}}
$$
$$
\sqrt[3]{\frac{a}{b+7}} + \sqrt[3]{\frac{b}{c+7}} + \sqrt[3]{\frac{c}{d+7}} + \sqrt[3]{\frac{d}{a+7}} \le \frac{8}{\sqrt[3]{7}}
$$