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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (I)

  • question_answer
    If \[a-\frac{1}{a-3}=5,\]then the value of  \[{{(a-3)}^{3}}-\frac{1}{{{(a-3)}^{3}}}\]is [SSC CGL Tier II, 2015]

    A) 7

    B) 5

    C) 2

    D) 14

    Correct Answer: D

    Solution :

    [d] \[a-\frac{1}{a-3}=5\]\[\Rightarrow \]\[a-3\frac{1}{a-3}=2\]             \[\Rightarrow \]\[{{(a-3)}^{3}}-{{\left( \frac{1}{a-3} \right)}^{3}}-3\,(a-3)\times \frac{1}{(a-3)}\left( a-3-\frac{1}{a-3} \right)=8\] \[\Rightarrow \]   \[{{(a-3)}^{3}}-\frac{1}{{{(a-3)}^{3}}}-3\times 2=8\] \[\therefore \]      \[{{(a\,-3)}^{3}}-\frac{1}{{{(a\,-3)}^{3}}}=8+6=14\]


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