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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Solution of quadratic equations and Nature of roots

  • question_answer
    If \[x=\sqrt{6+\sqrt{6+\sqrt{6+....\text{to}\,\,\infty }},}\] then  [Pb. CET 1999]

    A) x is an irrational number

    B) \[2<x<3\]

    C) \[x=3\]

    D) None of these

    Correct Answer: C

    Solution :

     \[x=\sqrt{6+x}\], \[x>0\,\,\Rightarrow {{x}^{2}}=6+x,x>0\] \[\Rightarrow {{x}^{2}}-x-6=0,\,x>0\] \[\Rightarrow x=3,x>0\].


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