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SSC Sample Paper Mock Test-13 SSC CGL Tear-II Paper-1

  • question_answer
    If \[x={{(\sqrt{2}+1)}^{-\,\,\frac{1}{3}}},\]then the value of\[\left( {{x}^{3}}-\frac{1}{{{x}^{3}}} \right)\]is

    A) 0 

    B)  \[-\,\,\sqrt{2}\]

    C)  \[-\,\,2\]

    D)  \[3\sqrt{2}\]

    Correct Answer: C

    Solution :

    \[x={{(\sqrt{2}+1)}^{\frac{1}{3}}}\]\[\Rightarrow \]\[{{x}^{-3}}=\sqrt{2}+1\] \[\Rightarrow \] \[{{x}^{3}}=\frac{1}{\sqrt{2}+1}=\frac{1(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}=\sqrt{2}-1\] \[\Rightarrow \] \[\frac{1}{{{x}^{3}}}=\sqrt{2}+1\] \[\therefore \] \[{{x}^{3}}-\frac{1}{{{x}^{3}}}=\sqrt{2}-1-\sqrt{2}-1=-2\]


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