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SSC Sample Paper SSC CGL - Sample Paper-9

  • question_answer
    \[\sqrt{6+\sqrt{6+\sqrt{6+........}}}\] is equal to

    A)  \[{{6}^{2/3}}\]                                  

    B)  6

    C)  \[3\frac{1}{2}\]                        

    D)  3

    Correct Answer: D

    Solution :

    Let        \[x=\sqrt{6+\sqrt{6+\sqrt{6+.............}}}\] or         \[x=\sqrt{6+x}\] or         \[{{x}^{2}}=6+x\] or         \[{{x}^{2}}-x-6=0\] or         \[{{x}^{2}}-3x+2x-6=0\] or         \[x(x-3)+2(x-3)=0\] or         \[(x+2)(x-3)=0\] \[\therefore \]      \[x=-\,2\] and x = 3


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