The range of function y = log 0.5 (x ^ 2 + 2x + a) is r, and the range of a is obtained

Let t = x ^ 2 + 2x + A, if the range of values is all real numbers, then t must be able to get all positive real numbers, and T = (x + 1) ^ 2 + A-1. Moreover, the symmetry axis of the graph is x = - 1, the opening is upward, and the intersection point with the Y axis is (0, A-1). Therefore, when A-1 ≤ 0, that is, a ≤ 1, there is a value range of X, so that t can get all positive real numbers, so that

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