2. Sample Papers
  3. 11th Class
  4. Mathematics

11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-7

  • question_answer
    If \[x=\sqrt{7+4\sqrt{3}}\]then \[x+\frac{1}{x}\]is equal to

    A)  2                   

    B)  3              

    C)  4                                

    D)  6

    Correct Answer: C

    Solution :

    [c] \[\because x=\sqrt{7+4\sqrt{3}}\] \[x=\sqrt{{{(2)}^{2}}+{{(3)}^{2}}+2.2\sqrt{3}}=\sqrt{{{(2+\sqrt{3})}^{2}}}=2+\sqrt{3}\] \[\therefore \frac{1}{x}=\frac{1}{2+\sqrt{3}}=\frac{2-\sqrt{3}}{{{(2)}^{2}}-{{(\sqrt{3})}^{2}}}=2-\sqrt{3}\] \[\therefore x+\frac{1}{x}=2+\sqrt{3}+2-\sqrt{3}=4\] Hence, option [c] is correct.


You need to login to perform this action.
You will be redirected in 3 sec spinner