Question

If \(x = \frac{2\sqrt{2}-\sqrt{7}}{2\sqrt{2}+\sqrt{7}}\), then \(x + x^{-1}\) is equal to

• A. 28
• B. 32
• C. 30
• D. 24

Hint:

Use symmetry identities for expressions like \(x + 1/x\).

Answer 1

The Correct Option is C

Concept: \[ x + \frac{1}{x} = \frac{(a-b)^2 + (a+b)^2}{a^2-b^2} \]

Step 1: Let.
\[ a = 2\sqrt{2}, \quad b = \sqrt{7} \]

Step 2: Compute.
\[ x + \frac{1}{x} = \frac{(a-b)^2 + (a+b)^2}{a^2-b^2} = \frac{2(a^2+b^2)}{a^2-b^2} \] \[ a^2 = 8, \quad b^2 = 7 \] \[ = \frac{2(15)}{1} = 30 \]