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SSC Sample Paper SSC CGL - Sample Paper-20

  • question_answer
    If \[x=\frac{\sqrt{3+1}}{\sqrt{3-1}},\] and \[y=\frac{\sqrt{3-1}}{\sqrt{3+1}},\] 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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