Question 128
Find all the $(x, y, z)$ triplets of real numbers which are solutions of the $$
\left.\begin{array}{l}
3 \cdot 2^{y}-1=2^{x}+2^{-x} \\
3 \cdot 2^{z}-1=2^{y}+2^{-y} \\
3 \cdot 2^{x}-1=2^{z}+2^{-z}
\end{array}\right\}
$$ equation system
\left.\begin{array}{l}
3 \cdot 2^{y}-1=2^{x}+2^{-x} \\
3 \cdot 2^{z}-1=2^{y}+2^{-y} \\
3 \cdot 2^{x}-1=2^{z}+2^{-z}
\end{array}\right\}
$$ equation system