I have a simple nonlinear system of equations that I want Mathematica to solve for. Here is what I try and it fails.
t = ArcCos[n1 * 2 / Pi / F]
b = x / Cos[t]
x = Pi * F / 2 / n2
y = Sqrt[b^2 - x^2]
x^-2 + y^-2 = 4
Namely after the fifth equation Mathematica responds with what appears to me as a warning
Set::write: Tag Plus in .... is Protected.
The solver dies with this output
Solve::eqf: 4 is not a well-formed equation.
The answer I expect is
n2 = sqrt(Pi^2*F^2-4*n1^2)
Of course there is +- sqrt(...) to take into account, but I also know the following about my system that lets me eliminate the other answer
n1 >= 0
n2 >= 0
Pi*F >= 2*n1
So in short I want Mathematica to solve the system for n2, and I also want it to isolate the only valid answer given the restrictions above.