Question 21
Find all triples $(x, y, z)$ of real numbers which are solutions of the system:
$$
\begin{cases} x^2 + y^2 + 25z^2 = 6xz + 8yz \\ 3x^2 + 2y^2 + z^2 = 240 \end{cases}
$$
$$
\begin{cases} x^2 + y^2 + 25z^2 = 6xz + 8yz \\ 3x^2 + 2y^2 + z^2 = 240 \end{cases}
$$