olymmath

ISL 2018 A7

    Find the maximal value of S=ab+73+bc+73+cd+73+da+73S=\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,da, b, c, d are nonnegative real numbers which satisfy a+b+c+d=100a+b+c+d=100.

    Dataset text NuminaMath olympiads. Quoted with source.

    Official text: IMO 2018 Shortlist booklet, page 5.

    Solutions

    Official solution Solution 1 by the IMO Problem Selection Committee

    The terms of the source let olymmath link to this solution but not copy it. Read the solution (IMO official site).

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