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SSC Sample Paper SSC CGL - Sample Paper-4

  • question_answer
    The value of \[\sqrt{2+\sqrt{2+\sqrt{2+...}}}\] is

    A)  2        

    B)  \[\sqrt{2}\]

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

    D)  \[2+\sqrt{2}\]

    Correct Answer: A

    Solution :

    Let        \[x=\sqrt{2+\sqrt{2+...\infty }}\] \[\Rightarrow \]   \[{{x}^{2}}=2+x\] \[\Rightarrow \]   \[{{x}^{2}}-x-2=0\] \[\Rightarrow \]   \[(x+1)(x-2)=0\] \[\Rightarrow \]   \[x=2\]              \[(\because \,x\ne -\,1)\]  


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