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3 variable equation

Source: Middle European Mathematical Olympiad 2012 - Team Compt. T-1

September 14, 2012
algebrasystem of equationsalgebra proposed

Problem Statement

Find all triplets (x,y,z) (x,y,z) of real numbers such that 2x3+1=3zx 2x^3 + 1 = 3zx 2y3+1=3xy 2y^3 + 1 = 3xy 2z3+1=3yz 2z^3 + 1 = 3yz
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