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8th Class Mathematics Algebraic Expressions Question Bank Algebraic Expressions & Identities

  • question_answer
    If \[x=3+2\sqrt{2}\]and \[\mathbf{xy}=\mathbf{1},\]then the value of \[\frac{{{x}^{2}}-3xy+{{y}^{2}}}{{{x}^{2}}+3xy+{{y}^{2}}}\]is

    A)  \[\frac{30}{31}\]                                  

    B)  \[\frac{70}{31}\]

    C)  \[\frac{35}{31}\]                                  

    D)  \[\frac{31}{37}\]

    Correct Answer: D

    Solution :

    (d) \[y=\frac{1}{x}=\frac{1}{3+2\sqrt{2}}=\frac{3-2\sqrt{2}}{9-8}=3-2\sqrt{2}\] Expression, \[\frac{{{x}^{2}}-3xy+{{y}^{2}}}{{{x}^{2}}+3xy+{{y}^{2}}}=\frac{{{\left( x-y \right)}^{2}}-xy}{{{\left( x+y \right)}^{2}}+xy}\] \[\Rightarrow x-y=(3+2\sqrt{2})-(3-2\sqrt{2})=4\sqrt{2}\] Also, \[x+y=6\] Expression= \[\frac{32-1}{36+1}=\frac{31}{37}.\]


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