Question : If $x+\frac{1}{x}=2$, then the value of $x^{57}+\frac{1}{x^{57}}$ is:
Option 1: 1
Option 2: –2
Option 3: 0
Option 4: 2
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Answer (1)
15th Jan, 2024
Correct Answer: 2
Solution :
Given, $x+\frac{1}{x}=2$
⇒ $x^2 + 1 = 2x$
⇒ $x^2-2x+1 = 0$
⇒ $(x-1)^2 = 0$
⇒ $x-1 = 0$
⇒ $x=1$
$\therefore x^{57}+\frac{1}{x^{57}}=1^{57}+\frac{1}{1^{57}} = 2$
Hence, the correct answer is 2.
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