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10th Class Mathematics Quadratic Equations Question Bank Quadratic Equations

  • question_answer
    If \[\sqrt{x-1}-\sqrt{x+1}+1=0,\] then 4x is equal to_____.

    A)  \[4\sqrt{-1}\]              

    B)  \[0\]                

    C)  5                    

    D)         \[1\frac{1}{4}\]                     

    Correct Answer: C

    Solution :

    Given equation is \[\sqrt{x-1}-\sqrt{x+1}=-1\]                 ...(1) Rationalizing (1), we get \[\frac{(x-1)-(x+1)}{\sqrt{x-1}+\sqrt{x+1}}=-1\] \[\Rightarrow \] \[\sqrt{x-1}+\sqrt{x+1}=2\] ?.(2) Adding (1) and (2), we get \[2\sqrt{x-1}=1\]  \[\Rightarrow \] \[x-1=\frac{1}{4}\] \[\Rightarrow \] \[4x=5\]


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