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3x3 system x^3-3x =4-y, 2y^3-6y=6-z, 3z^3-9z=8 -x (HOMC 2017 J Q8)

Source:

August 7, 2019

algebrasystem of equations

Problem Statement

Determine all real solutions

x, y, z

of the following system of equations:

\begin{cases} x^3 - 3x = 4 - y \\ 2y^3 - 6y = 6 - z \\ 3z^3 - 9z = 8 - x\end{cases}