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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (I)

  • question_answer
    If \[5a+\frac{1}{3a}=5,\]then the value of \[9{{a}^{2}}+\frac{1}{25{{a}^{2}}}\]is

    A) \[\frac{34}{5}\]

    B) \[\frac{39}{5}\]

    C) \[\frac{42}{5}\]

    D) \[\frac{52}{5}\]

    Correct Answer: B

    Solution :

    [b] Given,\[5a+\frac{1}{3a}=5\] \[\Rightarrow \]   \[\frac{5}{3}\left( 3a+\frac{1}{5a} \right)=5\] \[\Rightarrow \]   \[3a+\frac{1}{5a}=\frac{5\times 3}{5}=3\] On squaring both sides, we get \[9{{a}^{2}}+\frac{1}{25{{a}^{2}}}+2.3a.\frac{1}{5a}=9\] \[\Rightarrow \]   \[9{{a}^{2}}+\frac{1}{25{{a}^{2}}}=9-\frac{6}{5}=\frac{39}{5}\]


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