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max of y\sqrt{1-x}+z\sqrt{1-y}+x\sqrt{1-z} if 0<=x,y,z<=1

Source: 2021 Bosnia Herzegovina MO p1, posted as TST inside contest collections, 13.6.2021

October 7, 2022
algebrainequalitiesmax

Problem Statement

Let x,y,zx,y,z be real numbers from the interval [0,1][0,1]. Determine the maximum value of expression W=y⋅1−x+z⋅1−y+x⋅1−zW=y\cdot \sqrt{1-x}+z\cdot\sqrt{1-y}+x\cdot\sqrt{1-z}
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