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3-variable inequality

Source: Romanian DMO 8th grade P4

March 1, 2008
inequalitiesalgebra proposedalgebra

Problem Statement

Determine x,y,z>0 x,y,z>0 for which x^3y\plus{}3<\equal{}4z, y^3z\plus{}3<\equal{}4x,z^3x\plus{}3<\equal{}4y.