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SSC Sample Paper SSC CHSL (10+2) Sample Test Paper-25

  • question_answer
    The value of  \[\,\sqrt{12+\sqrt{12+\sqrt{12}}}+......\infty \] is -

    A)  3                                

    B)  4

    C) \[4.5\]                           

    D)  \[3.5\]

    Correct Answer: B

    Solution :

     Let \[x=\sqrt{12+\sqrt{12}+\sqrt{12}}+.......\infty \] \[x=\sqrt{12+x}\] Squaring both sides \[\Rightarrow \,\,\,\,{{x}^{2}}=12+x\] \[{{x}^{2}}-x-12=0\Rightarrow {{x}^{2}}-4x+3x-12=0\] \[x(x-4)+3(x-4)=0\Rightarrow (x+3)\,(x-4)=0\] So,  \[x=-3,4\,\,\,\Rightarrow \,x=\underline{\mathbf{4}}\]


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