The activity coefficients in a binary system are represented by \(\ln \gamma_{1}=A x_{2}^{2}\) and \(\ln \gamma_{2}=A x_{1}^{2}\). Show that if the system forms an azeotrope, the azeotropic composition is given by \(x_{1}=\frac{1}{2}\left(1+\frac{1}{A} \ln \frac{P_{1}^{\text {Sat }}}{P_{2}^{\text {Sat }}}\right)\)