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