Consider the following equations: $1-\frac{\mu}{1+x_{1}-x_{2}^{2}} = 0 \\ -2 + \frac{2 \mu x_{2}}{1+x_{1}-x_{2}^{2}}-\frac{\mu}{x_2} = 0$
Assume that $1+x_1-x_{2}^{2} \geq 0$ and $x_{2} \geq 0$. Solving for $x_2$ in terms of $\mu$ is just a matter of back substitution? In other words using the first equation to solve for $x_1$ in terms of $x_2$. Then substitute this into the second equation to get a quadratic in $x_2$?