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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (I)

  • question_answer
    If \[x+\frac{1}{x}=5,\]then the value of \[\frac{{{x}^{4}}+\frac{1}{{{x}^{2}}}}{{{x}^{2}}-3x+1}\]is

    A) 70

    B) 50

    C) 110

    D) 55

    Correct Answer: D

    Solution :

    [d] Given,\[x+\frac{1}{x}=5\] \[\Rightarrow \]   \[{{x}^{2}}-5x+1=0\] \[\Rightarrow \]   \[{{x}^{2}}-3x+1=2x\]                        …(i) \[\therefore \]      \[\frac{{{x}^{4}}+\frac{1}{{{x}^{2}}}}{{{x}^{2}}-3x+1}=\frac{x\left( {{x}^{3}}+\frac{1}{{{x}^{3}}} \right)}{2x}\]            [from Eq. (i)] \[=\frac{1}{2}\left( {{x}^{3}}+\frac{1}{{{x}^{3}}} \right)\] \[=\frac{1}{2}\left[ \left( x+\frac{1}{x} \right) \right]-3\left( x+\frac{1}{x} \right)\] \[=\frac{1}{2}[125-15]\] \[=55\]


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