Great Quadratic Equation

Algebra Level 5

Suppose that $x_1$ and $x_2$ are the positive real solution of $x^2 - bx + c = 0$ provided that $x_1^2 + \sqrt{x_2^2 - 2x_2} = 2x_1 - 1$ . Find the minimum value of $b+c$ .

Try this Hard Problem.

3 0 5 2 1 4 None of the choices