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SSC Quantitative Aptitude Basic Calculations Question Bank Square and Cube Root (II)

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

    A) \[\sqrt{2}\]

    B) 2

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

    D) \[2+\sqrt{2}\]

    Correct Answer: B

    Solution :

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


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