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Railways Sample Paper RRBs Assistant Loco Pilot and Technician CBT STAGE-I Sample Paper-33

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

    A)  2                    

    B)  3

    C)  \[2\sqrt{2}\]     

    D)         \[2\sqrt{3}\]

    Correct Answer: D

    Solution :

    Given, \[x=\sqrt{3}+\sqrt{2}\] \[\therefore \]\[\frac{1}{x}=\frac{1}{\sqrt{3}+\sqrt{2}}=\frac{1}{\sqrt{3}+\sqrt{2}}\times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}\] (on rationalizing) \[=\frac{\sqrt{3}-\sqrt{2}}{3-2}=\sqrt{3}-\sqrt{2}\]             \[\therefore \]\[x+\frac{1}{x}=\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}=2\sqrt{3}\]


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