Question 75
Find all triples $(x, y, z)$ of real numbers that satisfy the system
$$
\left\{\begin{array}{l}
x + y + z = 2008 \\
x^{2} + y^{2} + z^{2} = 6024^{2} \\
\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{2008}
\end{array}\right.
$$
$$
\left\{\begin{array}{l}
x + y + z = 2008 \\
x^{2} + y^{2} + z^{2} = 6024^{2} \\
\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{2008}
\end{array}\right.
$$