Gibbs-Duhem Equation
In a certain binary solution, the activity of component 1 is given by

R * ln(alpha_1) = R * ln(x_1) + A(x_2)^2 + B(x_2)^3

Where x_1 and x_2 are the respective mole fractions and A and B are constants. Derive an expression for alpha_2 (the activity of component 2) given that the equation above is valid over the entire concentration range. (Your answer should be in terms of R, A, B x_1, and x_2). A useful form of the Gibbs-Duhem Equation is

X1 * d * ln(alpha_1) + (x_2) * d * ln(alpha_2) = 0