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8th Class Mathematics Algebraic Expressions Question Bank Algebraic Expressions and Identities

  • question_answer
    Given that \[x-\frac{1}{x}=5,\] find the value of \[{{x}^{2}}+\frac{1}{{{x}^{2}}}\]

    A)  \[-27\]                                

    B)  \[23\]                  

    C)  \[-9\]                   

    D)         \[16\]

    Correct Answer: C

    Solution :

    \[x-\frac{1}{x}=5\] \[\Rightarrow \] \[{{\left( x-\frac{1}{x} \right)}^{2}}={{5}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+\frac{1}{{{x}^{2}}}-2=25\] \[\Rightarrow \] \[{{x}^{2}}+\frac{1}{{{x}^{2}}}=27\]


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