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9th Class Mathematics Number System and its Operations Question Bank Number System

  • question_answer
    If \[x=\sqrt[3]{2+\sqrt{3}}\],then \[{{\mathbf{x}}^{\mathbf{3}}}+\frac{1}{{{\mathbf{x}}^{\mathbf{3}}}},=\]

    A)  2                                

    B)  4

    C)  8                                

    D)  9

    Correct Answer: B

    Solution :

    (b): Given \[x=\sqrt[3]{2+\sqrt{3}}\] Take cube both side, are get \[{{x}^{3}}=2+\sqrt{3}\]                       ________ (1) \[\frac{1}{{{x}^{3}}}=\frac{1}{\left( 2+\sqrt{3} \right)}\times \frac{\left( 2-\sqrt{3} \right)}{\left( 2-\sqrt{3} \right)}\]     ______(2) \[\frac{1}{{{x}^{3}}}=2-\sqrt{3}\] So, \[{{x}^{3}}+\frac{1}{{{x}^{3}}}=2+\sqrt{3}+2-\sqrt{3}=4\]


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