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SSC Sample Paper SSC CGL - Sample Paper-7

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

    A)  14                   

    B)  13

    C)  15                               

    D)  10

    Correct Answer: A

    Solution :

    \[x=\frac{\sqrt{3}+1}{\sqrt{3}-1}=\frac{{{(\sqrt{3}+1)}^{2}}}{3-1}=\frac{3+1+2\sqrt{3}}{2}\] \[=2+\sqrt{3}\] And \[y=\frac{\sqrt{3}-1}{\sqrt{3}+1}=\frac{{{(\sqrt{3}-1)}^{2}}}{3-1}=\frac{3+1-2\sqrt{3}}{2}\]             \[=2-\sqrt{3}\] \[\therefore \]      \[{{x}^{2}}+{{y}^{2}}={{(2+\sqrt{3})}^{2}}+{{(2-\sqrt{3})}^{2}}\]                         \[=4+3+4\sqrt{3}+4+3-4\sqrt{3}\]                         \[=7+7=14\]


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