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3x3 system, x^2 + 4y^2 = 4zx , y^2 + 4z^2 = 4xy, z^2 + 4x^2 = 4yz

Source: Norwegian Mathematical Olympiad 2015 - Abel Competition p1a

September 3, 2019

system of equationsalgebra

Problem Statement

Find all triples

(x, y, z) \in R^3

satisfying the equations

\begin{cases} x^2 + 4y^2 = 4zx \\ y^2 + 4z^2 = 4xy \\ z^2 + 4x^2 = 4yz \end{cases}