Question : If $(a+\frac{1}{a})=–2$, then the value of $a^{1000}+a^{–1000}$ is:
Option 1: $2$
Option 2: $0$
Option 3: $1$
Option 4: $\frac{1}{2}$
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Correct Answer: $2$
Solution : Given: $(a+\frac{1}{a})= -2$ $⇒\frac{a^2+1}{a}=-2$ $⇒a^2+2a+1=0$ $⇒(a+1)^2=0$ $\therefore a= -1$ So, $a^{1000} + \frac{1}{a^{1000}} = 1+1=2$ Hence, the correct answer is $2$.
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