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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Solution of quadratic equations and Nature of roots

  • question_answer
    If \[x=\sqrt{7+4\sqrt{3}},\] then \[x+\frac{1}{x}=\] [EAMCET 1994]

    A) 4

    B) 6

    C) 3

    D) 2

    Correct Answer: A

    Solution :

    We have \[x=\sqrt{7+4\sqrt{3}}\] \ \[\frac{1}{x}=\frac{1}{\sqrt{7+4\sqrt{3}}}=\frac{\sqrt{7-4\sqrt{3}}}{\sqrt{7+4\sqrt{3}}.\sqrt{7-4\sqrt{3}}}\]                 \[=\sqrt{7-4\sqrt{3}}\] \\[x+\frac{1}{x}=\sqrt{7+4\sqrt{3}}+\sqrt{7-4\sqrt{3}}\]                \[=(\sqrt{3}+2)+(2-\sqrt{3})=4\].


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