Estimating $p$ from $A1$ and $A1$, system of equations, an estimation problem

Does anyone here know how $\rho$ is estimated in terms of $A_1, A_2 $ in the below equations, any mathematical procedure for this ..

$$ A_1 = \left | \alpha\; \left(\frac{ 1- e^{-j\cdot 2\cdot\pi \rho}}{j2\pi \rho}\right) \right|^2 $$

$$ A_2 = \left |\alpha\; \left(\frac{ 1- e^{-j\cdot 2\cdot\pi \rho}}{j2\pi+j2\pi \rho}\right) \right|^2 $$ $$ \rho=\frac{A_2+\sqrt(A_1A_2)}{A_1-A_2} $$

I am working on an estimation problem where from $A_1 , A_2 $ they estimated $p$ that is inside $A1$ and $A2$.

Anyone who could tell me about any mathematical procedure that how they did so?

According to what you wrote in comments $$\frac{A_1}{A_2}=\frac{(\rho +1)^2}{\rho ^2}$$ which is a quadratic in $\rho$.

Solve it and select the root you need.