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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 \[x=2+{{2}^{2/3}}+{{2}^{1/3}},\]then \[{{x}^{3}}-6{{x}^{2}}+6x=\] [MNR 1985]

    A) 3

    B) 2

    C) 1

    D) None of these

    Correct Answer: B

    Solution :

    \[x=2+{{2}^{2/3}}+{{2}^{1/3}}\,\,\,\,\Rightarrow x-2={{2}^{2/3}}+{{2}^{1/3}}\] Cubing both sides, we get \[{{x}^{3}}-8-6{{x}^{2}}+12x=6+6(x-2)\] Þ  \[{{x}^{3}}-6{{x}^{2}}+6x=2\].


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