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NTSE Sample Paper NTSE SAT Practice Test-17

  • question_answer
    If\[x=3+2\sqrt{2}\], then the value of \[\sqrt{x}-\frac{1}{\sqrt{x}}\]  is                             

    A) 1    

    B)                                  2   

    C) \[2\sqrt{2}\]                  

    D) \[3\sqrt{3}\]

    Correct Answer: B

    Solution :

    [b] We have, \[x=2+1+2\sqrt{2}\] \[={{(\sqrt{2}+1)}^{2}}\] \[\Rightarrow \,\sqrt{x}=\sqrt{2}+1\] Also, \[\frac{1}{\sqrt{x}}=\sqrt{2}-1\] \[\therefore \,\,\sqrt{x}-\frac{1}{\sqrt{x}}=\sqrt{2}+1-\sqrt{2}+1\] = 2


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