Solution
$$a + \frac{1}{a} = -2$$
let a = -1
-1 +$$\frac{1}{-1}$$ = -1+-1 = -2
$$\therefore a=-1$$
$$a^{1000} + a^{-1000}$$ = $$(-1)^{1000} + (-1)^{-1000}$$ = 1+1 = 2
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