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

  • question_answer
    If\[x=\sqrt[3]{2+\sqrt{3}}\], find the value of\[{{x}^{3}}+\frac{1}{{{x}^{3}}}\].

    A)  \[2\]                

    B)         \[4\]                

    C)  \[8\]                

    D)         \[9\]                            

    Correct Answer: B

    Solution :

    \[x=\sqrt[3]{2+\sqrt{3}}\] \[\Rightarrow \]\[{{x}^{3}}=2+\sqrt{3}\]and \[\frac{1}{{{x}^{3}}}=2-\sqrt{3}\] \[\therefore \]\[{{x}^{3}}+\frac{1}{{{x}^{3}}}=2+\sqrt{3}+2-\sqrt{3}=4\]


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