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

  • question_answer
    If \[a=\sqrt{3+\sqrt{3+\sqrt{3+...\infty }}},\] then which of the following is true?

    A) \[a=3\]

    B) \[3<a<4\]

    C) \[a>3\]

    D) \[2<a<3\]

    Correct Answer: D

    Solution :

    [d] \[a=\sqrt{3+a}\]\[\Rightarrow \]\[{{a}^{2}}=3+a\] \[\Rightarrow \] \[{{a}^{2}}-a-3=0\] \[\Rightarrow \]   \[a=\frac{1\pm \sqrt{1+12}}{2}=\frac{1\pm \sqrt{13}}{2}\]             \[=\frac{1\pm \sqrt{13}}{2}=\frac{1+3.6}{2}=\frac{4.6}{2}=2.3\] \[\therefore \]      \[2<a<3\]


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