Hkg TST

Algebra Difficulty 7.5 National Olympiad, round 2 Prove it Hong Kong

Find the maximal value of
$S = \sqrt[3]{\frac{a}{b+7}} + \sqrt[3]{\frac{b}{c+7}} + \sqrt[3]{\frac{c}{d+7}} + \sqrt[3]{\frac{d}{a+7}},$
where $a$ , $b$ , $c$ , $d$ are nonnegative real numbers which satisfy $a + b + c + d = 100$ .

Solution

(IMO Shortlist 2018 A7) See the official solution.

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