JEE Main & Advanced Sample Paper JEE Main Sample Paper-4

  • question_answer
    Given that\[\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}\]
    Statement-1: Given equation has no solution
    Statement-2: \[x=\frac{5}{4}\]is an extraneous solution of given equation.

    A)  Statement -1 is true, statement -2 is true and statement-2 is correct explanation for statement -1.

    B)  Statement -1 is true, statement -2 is true and Statement-2 is NOT correct explanation for statement -1.

    C)  Statement-1 is true, Statement-2 is false

    D)  Statement-1 is false, statement -2 is true

    Correct Answer: A

    Solution :

    On squaring we get \[x+1+x-1-2\sqrt{{{x}^{2}}-1}=4x-1\] \[-2\sqrt{{{x}^{2}}-1}=2x-1\] On again squaring we get \[4{{x}^{2}}-4=4{{x}^{2}}-4x+1\]\[\Rightarrow \]\[4x=5\]\[\Rightarrow \]\[x=\frac{5}{4}\] as if \[x=\frac{5}{4}\]- then second square root in given equation become imaginary, so no root is there.

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