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

  • question_answer
    If \[x=1-\sqrt{2},\]then find the value of \[{{\left( x-\frac{1}{x} \right)}^{2}}.\]

    A)  2                                

    B)  3                    

    C)  4                    

    D)         5

    Correct Answer: C

    Solution :

    We have, \[x=1-\sqrt{2}\] \[\therefore \]\[\frac{1}{x}=\frac{1}{1-\sqrt{2}}\times \frac{1+\sqrt{2}}{1+\sqrt{2}}=\frac{1+\sqrt{2}}{1-2}=-(1+\sqrt{2})\] Now, \[{{\left( x-\frac{1}{x} \right)}^{2}}={{(1-\sqrt{2}+1+\sqrt{2})}^{2}}={{(2)}^{3}}=4\]


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