Question : If $x+\frac{1}{x}=2$. Then, the value of $x^7+\frac{1}{x^5}$ is:
Option 1: $2^{12}$
Option 2: $2$
Option 3: $2^5$
Option 4: $2^7$
Answer (1)
14th Jan, 2024
Correct Answer: $2$
Solution :
Given: $x+\frac{1}{x}=2$
$x+\frac{1}{x} = 2$
In the above equation, substitute $x = 1$,
$1+\frac{1}{1} = 2$
Then, the value of $x^{7}+\frac{1}{x^{5}}$ is,
$1^{7}+\frac{1}{1^{5}} = 2$
Hence, the correct answer is 2.
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