MathDB

3

Part of 2009 Junior Balkan MO

Problems(1)

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

Source: JBMO 2009 Problem 3

6/27/2009
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}
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