8.5 The number of integers $x$ that satisfy the equation $\left(x^{2}-x-1\right)^{x+2}=1$ is
(A) 2.
(B) 3.
(C) 4.
(D) 5.
(E) None of the above conclusions is correct.
(36th American High School Mathematics Examination, 1985)
[Solution] By the properties of exponential functions and the given conditions, $x$ should satisfy $\left\{\begin{array}{l}x+2=0, \\ x^{2}-x-1 \neq 0 ;\end{array}\right.$ or $\left\{\begin{array}{l}x^{2}-x-1=-1, \\ x+2 \text { is even; }\end{array}\right.$ or $x^{2}-x-1=1$. Solving these respectively gives $x=-2, x=0, x=2$ and -1. Therefore, the answer is $(C)$.