Question

If \(x - \frac{1}{x} = 13\), then the value of \({x^2} + \frac{1}{{{x^2}}}\) is:
1. 165
2. 171
3. 167
4. 169

Answer 1

Correct Answer - Option 2 : 171

Given:

\(x - \frac{1}{x} = 13\)

Formula used:

If x – 1/x = K

Then on squaring both side we get

x2 + 1/x2 = k2 + 2

Calculation:

Apply the above formula 

⇒ (x - 1/x)² = 13²

⇒ x² + 1/x² = 169 + 2

⇒ x2 + 1/x2 = 171

∴ The value of x2 + 1/x2 is 171.