If \(x = \frac{\sqrt{a^2 + b^2} + \sqrt{a^2 - b^2}}{\sqrt{a^2 + b^2} - \sqrt{a^2 - b^2}}\), then —

Q.If \(x = \frac{\sqrt{a^2 + b^2} + \sqrt{a^2 - b^2}}{\sqrt{a^2 + b^2} - \sqrt{a^2 - b^2}}\), then — (a) \(b^2x^2-2a^2x-b^2=0\) (b) \(b^2x^2-2a^2x+b^2=0\) (c) \(b^2x^2+2a^2x+b^2=0\) (d) None of the above

Answer: B

Here’s the full English translation of your mathematical derivation: Let \[ x = \frac{\sqrt{a^2 + b^2} + \sqrt{a^2 - b^2}}{\sqrt{a^2 + b^2} - \sqrt{a^2 - b^2}} \] Then, \[ \frac{x + 1}{x - 1} = \frac{\sqrt{a^2 + b^2} + \sqrt{a^2 - b^2}}{\sqrt{a^2 + b^2} + \sqrt{a^2 - b^2}} + \frac{\sqrt{a^2 + b^2} - \sqrt{a^2 - b^2}}{-\sqrt{a^2 + b^2} + \sqrt{a^2 - b^2}} \]