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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (II)

  • question_answer
    If \[a+\frac{1}{a}+2=0,\]then the value of \[{{a}^{37}}-\frac{1}{{{a}^{100}}}\]is

    A) \[0\]

    B) \[-\,2\]

    C) \[1\]

    D) \[2\]

    Correct Answer: B

    Solution :

    [b] \[a+\frac{1}{a}+2=0\] \[\Rightarrow \]   \[{{a}^{2}}+1+2a=0\] \[\Rightarrow \]   \[{{(a+1)}^{2}}=0\] \[\Rightarrow \]   \[a=-1\] \[\therefore \]      \[{{a}^{37}}-\frac{1}{{{a}^{100}}}=-1-\left( \frac{1}{1} \right)=-1-1=-2\]


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