Question : If $x+\frac{1}{x}=2$, then the value of $x^{2}+\frac{1}{x^{6}}$ is equal to:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: 3
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Answer (1)
22nd Jan, 2024
Correct Answer: 2
Solution :
Given: $x+\frac{1}{x}=2$
Putting the value of $x$ = 1, the above equation is satisfied.
Now, putting $x$ = 1 in the given equation, we get
$x^{2}+\frac{1}{x^{6}}$ = $1^{2}+\frac{1}{1^{6}}$ = 2
Hence, the correct answer is 2.
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