Question

If \(x - \frac{1}{x} = 2\), then what is the value of \(x^2 + \frac{1}{x^2}\)?

• A. 4
• B. 5
• C. 3
• D. 6

Hint:

Squaring expressions of the form \(x \pm \frac{1}{x}\) is a common technique to find higher powers.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Use the identity \((x - \frac{1}{x})^2 = x^2 + \frac{1}{x^2} - 2\).

Step 2: Detailed Explanation:
Given \(x - \frac{1}{x} = 2\). Squaring:
\((x - \frac{1}{x})^2 = 4\)
\(x^2 + \frac{1}{x^2} - 2 = 4\)
\(x^2 + \frac{1}{x^2} = 6\)

Step 3: Final Answer:
\(x^2 + \frac{1}{x^2} = 6\).