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

  • question_answer
    If \[\mathbf{x}+\frac{1}{x}=\mathbf{4}\], find the value of \[{{\mathbf{x}}^{\mathbf{2}}}+\frac{1}{{{\mathbf{x}}^{\mathbf{2}}}}\]

    A)  16                               

    B)  18             

    C)  14     

    D)  12

    Correct Answer: C

    Solution :

    (c): \[x+\frac{1}{x}=4\] \[\Rightarrow {{\left( x+\frac{1}{x} \right)}^{2}}=16={{x}^{2}}+\frac{1}{{{x}^{2}}}+2=16\] \[\Rightarrow {{x}^{2}}+\frac{1}{{{x}^{2}}}=14.\]


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