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Suppose that x1x_1x1 and x2x_2x2 are the positive real solution of x2−bx+c=0x^2 - bx + c = 0x2−bx+c=0 provided that x12+x22−2x2=2x1−1x_1^2 + \sqrt{x_2^2 - 2x_2} = 2x_1 - 1x12+x22−2x2=2x1−1. Find the minimum value of b+cb+cb+c.
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