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Railways R.R.C. (Hajipur) Solved Paper Held on 1st Shift 30-11-2014

  • question_answer
    \[If\,x=(3-\sqrt{5}),then({{x}^{2}}+\frac{16}{{{x}^{2}}})=?\]

    A) 30                                

    B) 28

    C) 26                                

    D) 24

    Correct Answer: B

    Solution :

    If                      \[x=3-\sqrt{5}\] \[{{x}^{2}}=14-6\sqrt{5}\] And                  \[\frac{1}{{{x}^{2}}}=\frac{1}{14-6\sqrt{5}}\times \frac{14+6\sqrt{5}}{14+6\sqrt{5}}\] \[=\frac{14+6\sqrt{5}}{16}\] \[\frac{16}{{{x}^{2}}}=14+6\sqrt{5}\] Then,                \[{{x}^{2}}+\frac{16}{{{x}^{2}}}=14-6\sqrt{5}+14+6\sqrt{5}\] \[=28\]  


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