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Given that two equations x2 + 2bx + a = 0 and X2 + ax + 2B have and only have one common root, then the minimum value of A2 + B2 is
Let m be the common root of the equation. Then M2 + 2bm + a = 0 (1), M2 + am + 2B = 0 (2) (1) - (2) get (m-1) (2b-a) = 0, so m = 1 or 2B = A. when 2B equals a, (1) (2) two equations are the same equation, and (1) (2) only have one common root, so m = 1. So 2B + A + 1 = 0. So a = - 1-2b. So A2 + B2
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