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Solution: X 1=0, X2=-4 is the solution from x 2+4x = 0, so A={0, -4}.

(1) When A crosses B=B, we can know that the elements in B set are less than or equal to those in A set ... Situation discussion:

When B is an empty set, it is satisfied that A crosses B=B, and then △ < 0, that is, [2 (a+1)] 2-4 (a 2-1) = 8a+8.

When b has only one element, △=0, a=- 1 can be obtained, and the expression of b becomes X 2 = 0, that is, B = {0 };;

When b has two elements, that is, when B={0, -4}, △ >; 0, get a>- 1,

According to the relationship between roots and coefficients, we can get that the solutions of 0+(-4)=-2(a+ 1), 0x (-4) = a 2-1and a= 1 are consistent.

To sum up, the value of a satisfying a = b is a.

(2) According to the combination of A and B=B, B has at least two elements, and the expression of B is a quadratic equation, so there are only two elements at most. Combined with the conclusion that B has two elements in (1), the value of A is 1.

Answer over!