Question 31
Let $x$, $y$, $z$ be nonzero real numbers with
$$
\frac{ x + y }{ z } = \frac{ y + z }{ x } = \frac{ z + x }{ y }.
$$
Determine all possible values of
$$
\frac{ (x + y)(y + z)(z + x) }{ xyz }.
$$
$$
\frac{ x + y }{ z } = \frac{ y + z }{ x } = \frac{ z + x }{ y }.
$$
Determine all possible values of
$$
\frac{ (x + y)(y + z)(z + x) }{ xyz }.
$$