Question 88
The real numbers $x$, $y$ and $z$ are not all equal and they satisfy
$$
x + \frac{1}{y} = y + \frac{1}{z} = z + \frac{1}{x} = k
$$
Determine all possible values of $k$.
$$
x + \frac{1}{y} = y + \frac{1}{z} = z + \frac{1}{x} = k
$$
Determine all possible values of $k$.