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

  • question_answer
    If \[\left( \mathbf{a}+\mathbf{b} \right)=\mathbf{5},\] then find \[{{\mathbf{a}}^{\mathbf{2}}}-\mathbf{ab}+{{\mathbf{b}}^{\mathbf{2}}}\] (given \[{{\mathbf{a}}^{\mathbf{3}}}+{{\mathbf{b}}^{\mathbf{3}}}=\mathbf{8}\])

    A)  1.6       

    B)  2

    C)  3                                

    D)  0

    Correct Answer: A

    Solution :

    (a): \[a+b=5\] While \[{{a}^{3}}+{{b}^{3}}=\left( a+b \right)\left( {{a}^{2}}-ab+{{b}^{2}} \right)\] \[\Rightarrow 8=5({{a}^{2}}-ab+{{b}^{2}})\] \[\therefore \left( {{a}^{2}}-ab+{{b}^{2}} \right)=\frac{8}{5}=1.6\]    


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