Question 131
If $x$, $y$, $k$ are positive reals such that
$$
3 = k^{2}\left(\frac{x^{2}}{y^{2}} + \frac{y^{2}}{x^{2}}\right) + k\left(\frac{x}{y} + \frac{y}{x}\right),
$$
find the maximum possible value of $k$.
$$
3 = k^{2}\left(\frac{x^{2}}{y^{2}} + \frac{y^{2}}{x^{2}}\right) + k\left(\frac{x}{y} + \frac{y}{x}\right),
$$
find the maximum possible value of $k$.