Correct Answer: Option B

Explanation

Given that  \(x + \frac{1}{x} = 8\)

We want to find 

\(x^2 + \frac{1}{x^2}\)

We can use the identity:

\(x^2 + \frac{1}{x^2} = \left( x + \frac{1}{x} \right)^2 - 2\)

Substituting the given value:

\(x^2 + \frac{1}{x^2} = 8^2 - 2\)

Calculating \( 8^2 \):

\(8^2 = 64\)

Now substituting back:

\(x^2 + \frac{1}{x^2} = 64 - 2 = 62\)

Thus, the final answer is \(x^2 + \frac{1}{x^2} = 62\)

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