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: $\frac{1}{2}$
Answer (1)
22nd Jan, 2024
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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