Question 73
If for the real numbers $x$, $y$, $z$, $k$ the following conditions are valid, $x \neq y \neq z \neq x$ and
$$
x^{3} + y^{3} + k(x^{2} + y^{2}) = y^{3} + z^{3} + k(y^{2} + z^{2}) = z^{3} + x^{3} + k(z^{2} + x^{2}) = 2008,
$$
find the product $x y z$.
$$
x^{3} + y^{3} + k(x^{2} + y^{2}) = y^{3} + z^{3} + k(y^{2} + z^{2}) = z^{3} + x^{3} + k(z^{2} + x^{2}) = 2008,
$$
find the product $x y z$.