• If x = \( \Large \sqrt{3} + \sqrt{2} \), then the value of \( \Large \left(x + \frac{1}{x}\right) \) is

    A) 2

      B) 3

    C) \( \Large 2\sqrt{2} \)

      D) \( \Large 2\sqrt{3} \)

    Correct Answer:
      D) \( \Large 2\sqrt{3} \)

    Description for Correct answer

    Given, \( \Large x = \sqrt{3} + \sqrt{2} \)

    Therefore, \( \Large \frac{1}{x} = \frac{1}{ \left(\sqrt{3}+\sqrt{2}\right) } \times \frac{ \left(\sqrt{3} - \sqrt{2}\right) }{ \left(\sqrt{3} - \sqrt{2}\right) } \) [rationalizing]

     \( \Large = \frac{1}{x} = \frac{\sqrt{3} - \sqrt{2}}{3 - 2} \)

    Therefore, \( \Large x+\frac{1}{x} = \sqrt{3} + \sqrt{2} + \sqrt{3} - \sqrt{2} = 2\sqrt{3} \)


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