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at least one of (1 - x)y, $(1 - y)z, (1 - z)x <= 1/4 if 0<x,y,z<1

Source: 1961 Hungary - Kürschák Competition p2

October 11, 2022
inequalitiesalgebra

Problem Statement

x,y,zx, y, z are positive reals less than 11. Show that at least one of (1−x)y(1 - x)y, (1−y)z(1 - y)z and (1−z)x(1 - z)x does not exceed 14\frac14 .
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