IMO Shortlist 2018 problem A7


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3. listopada 2019.
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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.

Izvor: https://www.imo-official.org/problems/IMO2018SL.pdf