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Symmetric system of equations: x(x-y)(x-z)=3

Source: Romanian District Olympiad 2002, Grade X, Problem 2

October 7, 2018
algebrasystem of equations

Problem Statement

Solve in C3 \mathbb{C}^3 the following chain of equalities: x(x−y)(x−z)=y(y−x)(y−z)=z(z−x)(z−y)=3. x(x-y)(x-z)=y(y-x)(y-z)=z(z-x)(z-y)=3.
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