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JEE Main & Advanced Mathematics Sets Question Bank Mock Test - Sets

  • question_answer
    Number of solutions of the equation \[\left| 2-\left| x \right| \right|=x+4\] is _________.

    A) 2

    B) 4

    C) 1

    D) 5

    Correct Answer: C

    Solution :

    [1] \[\left| 2-\left| x \right| \right|=x+4\]                   ...(i) \[\Rightarrow \,2-\left| x \right|=x+4\]                  ...(ii) Or \[\left| x \right|-2=x+4\]        ...(iii) From (i), 2-x=x+4 or x=-1. But this value doses not satisfy (i). From (iii), -x-2=x+4 or x=-3, which satisfies(i). So, equation has only one solution.


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