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

  • question_answer
    If \[\mathbf{a}+\frac{1}{a}=\frac{17}{4}\]then the value of \[\mathbf{a}-\frac{1}{a}\]is

    A)  4                                

    B)  13/4             

    C)  17/4                            

    D)  15/4

    Correct Answer: D

    Solution :

    (d): \[a+\frac{1}{a}=\frac{17}{4}\] Squaring, \[{{a}^{2}}+2+\frac{1}{{{a}^{2}}}=\frac{289}{16}\] Subtracting '4', we get \[{{a}^{2}}-2+\frac{1}{{{a}^{2}}}=\frac{289-64}{16}\] \[\Rightarrow {{\left( a-\frac{1}{a} \right)}^{2}}={{\left( \frac{15}{4} \right)}^{2}}\,\,\,\,\,\Rightarrow a-\frac{1}{a}=\frac{15}{4}\].


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