Question

Q. Let \( S=\left\{x: x \in R\right. \) and \( \left.(\sqrt{3}+\sqrt{2})^{x^{2}-4}+(\sqrt{3}-\sqrt{2})^{x^{2}-4}=10\right\} \) Then \( n ( S ) \) is equal to A 2 B 4 C 6 D 0

Answer 1

Correct option is (B) 4

Let \((\sqrt 3 + \sqrt 2)^{x^2 - 4} = t\)

\(t + \frac 1t = 10\)

⇒ \(t = 5 + 2\sqrt6, 5-2\sqrt6\)

⇒ \((\sqrt 3 + \sqrt 2)^{x^2 - 4} = 5 + 2\sqrt 6, 5 - 2\sqrt 6\)

⇒ \(x^2 - 4 = 2, -2\) or \(x^2 = 6, 2\)

⇒ \(x = \pm \sqrt 2, \pm \sqrt 6\)