JBMO-SL 2013 A1

Find all ordered triples $(x, y, z)$ of real numbers satisfying the following system of equations:

$\begin{aligned} x^{3} & =\frac{z}{y}-2 \frac{y}{z} \\ y^{3} & =\frac{x}{z}-2 \frac{z}{x} \\ z^{3} & =\frac{y}{x}-2 \frac{x}{y} \end{aligned}$

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

(1,1,-1),(1,-1,1),(-1,1,1),(-1,-1,-1)

Solutions

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