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1a

Part of 2015 Abels Math Contest (Norwegian MO) Final

Problems(1)

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

9/3/2019
Find all triples (x,y,z)∈R3(x, y, z) \in R^3 satisfying the equations {x2+4y2=4zxy2+4z2=4xyz2+4x2=4yz\begin{cases} x^2 + 4y^2 = 4zx \\ y^2 + 4z^2 = 4xy \\ z^2 + 4x^2 = 4yz \end{cases}
system of equationsalgebra