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

  • question_answer
    If \[x=3+\sqrt{8},\] the value of \[\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)\] is

    A)  \[32\sqrt{2}\]

    B)  \[34\]

    C)  38

    D)  \[40\sqrt{2}\]

    Correct Answer: B

    Solution :

    \[\frac{1}{x}=\frac{1}{3+\sqrt{8}}=\frac{3-\sqrt{8}}{(3+\sqrt{8})(3-\sqrt{8})}=\frac{3-\sqrt{8}}{9-8}=3-\sqrt{8}\]\[\therefore \] \[{{x}^{2}}+\frac{1}{{{x}^{2}}}={{\left( x+\frac{1}{x} \right)}^{2}}-2\] \[={{(3+\sqrt{8}+3-\sqrt{8})}^{2}}-2\] \[={{(6)}^{3}}-2=36-2=34\]


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