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Railways Sample Paper RRB (Group D) Sample Test Paper-4

  • question_answer
    The value of \[\left( \sqrt{6+\sqrt{6+\sqrt{6+.....upto...}}} \right)\]is equal to

    A)  3                    

    B)  10

    C)  8                      

    D)  2

    Correct Answer: A

    Solution :

    [a] \[x=\sqrt{6+\sqrt{6+\sqrt{6+........\infty }}}\] On squaring, \[{{x}^{2}}=6+\sqrt{6+\sqrt{6+..........\infty }}\] \[\Rightarrow \,\,\,{{x}^{2}}=6+x\] \[\Rightarrow \,\,\,{{x}^{2}}-\,x-\,6=0\] \[\Rightarrow \,\,\,{{x}^{2}}-\,3x+2x-\,6=0\] \[\Rightarrow x\,\,(x-3)+2(x-3)=0\] \[\Rightarrow (x-3)\,\,(x+2)=0\] \[\Rightarrow x=3\,\,because\,\,x\ne -2\] By trick \[3\times 2=6\] Let the number be x and y.


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