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

  • question_answer
    If \[\mathbf{x=}\frac{\sqrt{\mathbf{2}}\mathbf{+}\sqrt{\mathbf{1}}}{\sqrt{\mathbf{2}}\mathbf{-}\sqrt{\mathbf{1}}}\] and \[y\mathbf{=}\frac{\sqrt{\mathbf{2}}-\sqrt{\mathbf{1}}}{\sqrt{\mathbf{2}}+\sqrt{\mathbf{1}}}\], find the value of \[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-}{{\mathbf{y}}^{\mathbf{2}}}\]

    A)  96                               

    B)  34   

    C)  10                               

    D)  \[2\sqrt{2}\]

    Correct Answer: B

    Solution :

    (b): \[x=\frac{\sqrt{2}+\sqrt{1}}{\sqrt{2}-\sqrt{1}}\times \frac{\sqrt{2}+\sqrt{1}}{\sqrt{2}+\sqrt{1}}\] \[\frac{{{\left( \sqrt{2}+\sqrt{1} \right)}^{2}}}{2-1}\] \[\Rightarrow x=2+1+2\sqrt{2}\Rightarrow x=3+2\sqrt{2}\] And similarly \[y=3-2\sqrt{2}\] \[{{x}^{2}}+{{y}^{2}}={{\left( x+y \right)}^{2}}-2xy={{\left( 6 \right)}^{2}}-2(9-8)=34\]         


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