MathDB
xyz = (1 - x)(1 - y)(1 - z)

Source: JBMO 2009 Problem 3

June 27, 2009
symmetryinequalities proposedinequalities

Problem Statement

Let x x, y y, z z be real numbers such that 0<x,y,z<1 0 < x,y,z < 1 and xyz \equal{} (1 \minus{} x)(1 \minus{} y)(1 \minus{} z). Show that at least one of the numbers (1 \minus{} x)y,(1 \minus{} y)z,(1 \minus{} z)x is greater than or equal to 14 \frac {1}{4}
Back to ProblemsView on AoPS