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

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

    A)  49                               

    B)  34   

    C)  100                             

    D)  102

    Correct Answer: B

    Solution :

    (b): \[b=\frac{1}{a}=\frac{1}{3+2\sqrt{2}}=3-2\sqrt{2}\] \[\therefore \,\,{{a}^{2}}+{{b}^{2}}={{(3+2\sqrt{2})}^{2}}+{{(3-2\sqrt{2})}^{2}}\] \[=2({{3}^{2}}+{{(2\sqrt{2})}^{2}}=34\]         


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