Let $x, y, z$ be positive numbers such that $xyz \le 2$ and $\frac{1}{x^2}+ \frac{1}{y^2}+ \frac{1}{z^2}< k$, for some real $k \ge 2$. Find all values of $k$ such that the conditions above imply that there exist a triangle having the side-lengths $x, y, z$.