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Omni-MATH / Find all triples (x,y,z) of real numbers that satisfy the system of equations

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Find all triples

(x,y,z)

of real numbers that satisfy the system of equations

\[ \begin{cases}x^3 \equal{} 3x\minus{}12y\plus{}50, \\ y^3 \equal{} 12y\plus{}3z\minus{}2, \\ z^3 \equal{} 27z \plus{} 27x. \end{cases}\]

[i]Razvan Gelca.[/i]

Plain-text mathematical notation (without MathML)

Find all triples (x,y,z) of real numbers that satisfy the system of equations
\[ \begin{cases}x^3 \equal{} 3x\minus{}12y\plus{}50, \\ y^3 \equal{} 12y\plus{}3z\minus{}2, \\ z^3 \equal{} 27z \plus{} 27x. \end{cases}\]

[i]Razvan Gelca.[/i]

Original LaTeX notation

Find all triples $ (x,y,z)$ of real numbers that satisfy the system of equations
\[ \begin{cases}x^3 \equal{} 3x\minus{}12y\plus{}50, \\ y^3 \equal{} 12y\plus{}3z\minus{}2, \\ z^3 \equal{} 27z \plus{} 27x. \end{cases}\]

[i]Razvan Gelca.[/i]

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task_id: 1f0c4419-a430-5937-9733-fb0d39d51475
task_key: test--1f0c4419-a430-5937-9733-fb0d39d51475
task_revision_id: 2
config / split: / test

Official source

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