Question 89
Let $x, y, z$ be real numbers such that
$$
\frac{1}{|x^2 + 2yz|}, \quad \frac{1}{|y^2 + 2zx|}, \quad \frac{1}{|z^2 + 2xy|}
$$
are side-lengths of a (non-degenerate) triangle. Find all possible values of $xy + yz + zx$.
(Michal Rolínek)
$$
\frac{1}{|x^2 + 2yz|}, \quad \frac{1}{|y^2 + 2zx|}, \quad \frac{1}{|z^2 + 2xy|}
$$
are side-lengths of a (non-degenerate) triangle. Find all possible values of $xy + yz + zx$.
(Michal Rolínek)