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Railways Sample Paper RRBs Assistant Loco Pilot and Technician CBT STAGE-I Sample Paper-31

  • question_answer
    If \[x=2+\sqrt{3}\] and \[y=2-\sqrt{3}\] then the value of\[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{3}}+{{y}^{3}}}\]is

    A)  \[\frac{7}{38}\]            

    B)  \[\frac{7}{40}\]

    C)  \[\frac{7}{19}\]            

    D)  \[\frac{7}{26}\]

    Correct Answer: D

    Solution :

    \[x=2+\sqrt{3},y+2-\sqrt{3}\] \[x+y=4\] \[xy=4-3=1\] \[\therefore \]      \[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}+{{y}^{3}}}=\frac{{{(x+y)}^{2}}-2xy}{{{(x+y)}^{3}}-3xy(x+y)}\] \[=\frac{16-2}{64-3\times 4}=\frac{14}{52}=\frac{7}{26}\]


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