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

  • question_answer
    If \[x=(7+4\sqrt{3}),\]then \[\left( x+\frac{1}{x} \right)=\_\_\_\_\_.\]

    A) \[8\sqrt{3}\]                              

    B)  14       

    C)  49                   

    D)         48       

    Correct Answer: B

    Solution :

    We have, \[x=7+4\sqrt{3}\] Now, \[\frac{1}{x}=\frac{1}{7+4\sqrt{3}}\times \frac{7-4\sqrt{3}}{7-4\sqrt{3}}\] \[=\frac{7-4\sqrt{3}}{49-48}=7-4\sqrt{3}\] \[\therefore \]\[x+\frac{1}{x}=7+4\sqrt{3}+7-4\sqrt{3}=14\]


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