Question 75

If $$a + \frac{1}{a} = -2$$ then the value of $$a^{1000} + a^{-1000}$$ is

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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