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

  • question_answer
    If HCF and LCM of two terms a and b are x and y respectively and \[\mathbf{a}+\mathbf{b}=\mathbf{x}+\mathbf{y},\]then \[{{\mathbf{x}}^{\mathbf{2}}}+{{\mathbf{y}}^{\mathbf{2}}}\]= ?

    A)  \[{{a}^{2}}-{{b}^{2}}\]                   

    B)  \[2{{a}^{2}}+{{b}^{2}}\]         

    C)  \[{{a}^{2}}+{{b}^{2}}\]

    D)  \[{{a}^{2}}+2{{b}^{2}}\]

    Correct Answer: C

    Solution :

       (c): \[HCF\times LCM=\]Product of nos. \[\Rightarrow x\times y=a\times b\] Also, \[a+b=x+y\] Squaring \[{{\left( x+y \right)}^{2}}={{(a+b)}^{2}}\] \[{{x}^{2}}+{{y}^{2}}+2xy={{a}^{2}}+{{b}^{2}}+2ab\] But \[xy=ab\] \[\Rightarrow {{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}.\]            


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