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

  • question_answer
    The minimum value of \[\frac{{{x}^{4}}+{{y}^{4}}+{{z}^{2}}}{xyz}\] for positive real number x, y, z is

    A) \[\sqrt{2}\]

    B) \[2\sqrt{2}\]

    C) \[4\sqrt{2}\]

    D) \[8\sqrt{2}\]

    Correct Answer: B

    Solution :

    [b] By \[A.M.\ge GM.\] \[{{x}^{4}}+{{y}^{4}}\ge 2{{x}^{2}}{{y}^{2}}\] and \[2{{x}^{2}}{{y}^{2}}+{{z}^{2}}\ge \sqrt{8}\,\,xyz.\] \[\Rightarrow \,\,\,\,\,\,\frac{{{x}^{4}}+{{y}^{4}}+{{z}^{2}}}{xyz}\ge \sqrt{8}\]


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