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KVPY Sample Paper KVPY Stream-SX Model Paper-30

  • question_answer
    If \[x=2+{{2}^{2/3}}+{{2}^{1/3}}\], then the value of \[{{x}^{3}}-6{{x}^{2}}+6x\] is

    A) 3

    B) 2               

    C) 1         

    D) None of these

    Correct Answer: B

    Solution :

    Solution we have \[x=2+{{2}^{2/3}}+{{2}^{1/3}}\]\[\Rightarrow x-2={{2}^{2/3}}+{{2}^{1/3}}\]\[\Rightarrow {{(x-2)}^{3}}={{2}^{2}}+2+{{3.2}^{2/3}}{{2}^{1/3}}({{2}^{2/3}}+{{2}^{1/3}})\]
    \[\Rightarrow {{x}^{3}}-6{{x}^{2}}+12x-8=4+2+3\,\,x\,\,2\,\,x\,\,(x-2)\]\[\Rightarrow {{x}^{3}}-6{{x}^{2}}+6x=2.\]


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