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SSC Sample Paper SSC CGL - Sample Paper-14

  • question_answer
    \[\sqrt{2+\sqrt{2+\sqrt{2+.......}}}\] is equal to

    A) 1.42                 

    B) 4

    C) 2                     

    D) 2.414

    Correct Answer: C

    Solution :

    Let \[=\sqrt{2+\sqrt{2+\sqrt{2+.....}}}\] \[={{x}^{2}}=2+\sqrt{2+\sqrt{2+\sqrt{2+.....}}}\] \[={{x}^{2}}=2+x\] \[={{x}^{2}}-x-2=0\] \[={{x}^{2}}-2x+x-2=0\] \[x(x-2)+1(x-2)=0\] \[\Rightarrow \] \[(x-2)(x+1)=0\] \[\Rightarrow \] \[x=2,\] because the numbers are positive   


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