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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 \[{{x}^{2/3}}-7{{x}^{1/3}}+10=0,\] then \[x=\] [BIT Ranchi 1992]

    A) {125}

    B) {8}

    C) \[\varphi \]

    D) {125, 8}

    Correct Answer: D

    Solution :

    Given that\[{{x}^{2/3}}-7{{x}^{1/3}}+10=0\]. Given equation can be written as \[{{({{x}^{1/3}})}^{2}}-7({{x}^{1/3}})+10=0\] Let\[a={{x}^{1/3}}\], then it reduces to the equation \[{{a}^{2}}-7a+10=0\,\,\Rightarrow (a-5)(a-2)=0\,\,\,\Rightarrow a=5,\,2\] Putting these values, we have \[{{a}^{3}}=x\,\,\,\,\Rightarrow x=125\]and 8.


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