Question 21
Determine all triples of real numbers $(x, y, z)$ that satisfy the following system of equations:
$$
\begin{aligned}
xyz &= 8, \\
x^2y + y^2z + z^2x &= 73, \\
x(y - z)^2 + y(z - x)^2 + z(x - y)^2 &= 98.
\end{aligned}
$$
$$
\begin{aligned}
xyz &= 8, \\
x^2y + y^2z + z^2x &= 73, \\
x(y - z)^2 + y(z - x)^2 + z(x - y)^2 &= 98.
\end{aligned}
$$