JEE Main & Advanced Mathematics Sequence & Series Question Bank Self Evaluation Test - Sequences and Series

  • question_answer
    If \[a=1+(\sqrt{3}-1)+{{(\sqrt{3}-1)}^{2}}+{{(\sqrt{3}-1)}^{3}}+....\] and\[ab=1\], then a and bare the roots of the equation

    A) \[{{x}^{2}}+4x-1=0\]

    B)

    C) \[{{x}^{2}}+4x+1=0\]

    D) \[{{x}^{2}}-4x+1=0\]

    Correct Answer: D

    Solution :

    [d] \[a=\frac{1}{1-\left( \sqrt{3}-1 \right)}=\frac{1}{2-\sqrt{3}}=2+\sqrt{3}\] and \[ab=1\Rightarrow b=2-\sqrt{3}\] so, a and b are roots of \[{{x}^{2}}-4x+1=0\]


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