Question 89
Let $a$, $b$, $c$, $x$, $y$, and $z$ be complex numbers such that
$$
a = \frac{b+c}{x-2}, \quad b = \frac{c+a}{y-2}, \quad c = \frac{a+b}{z-2}.
$$
If $xy + yz + zx = 67$ and $x + y + z = 2010$, find the value of $xyz$.
$$
a = \frac{b+c}{x-2}, \quad b = \frac{c+a}{y-2}, \quad c = \frac{a+b}{z-2}.
$$
If $xy + yz + zx = 67$ and $x + y + z = 2010$, find the value of $xyz$.