Question 72
Find all triples of positive real numbers $(x, y, z)$ which satisfy the system
$$
\begin{cases}
\sqrt[3]{x} - \sqrt[3]{y} - \sqrt[3]{z} = 64 \\
\sqrt[4]{x} - \sqrt[4]{y} - \sqrt[4]{z} = 32 \\
\sqrt[6]{x} - \sqrt[6]{y} - \sqrt[6]{z} = 8
\end{cases}
$$
$$
\begin{cases}
\sqrt[3]{x} - \sqrt[3]{y} - \sqrt[3]{z} = 64 \\
\sqrt[4]{x} - \sqrt[4]{y} - \sqrt[4]{z} = 32 \\
\sqrt[6]{x} - \sqrt[6]{y} - \sqrt[6]{z} = 8
\end{cases}
$$