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

  • question_answer
    If \[{{\mathbf{a}}^{\mathbf{2}}}+{{\mathbf{b}}^{\mathbf{2}}}+{{\mathbf{c}}^{\mathbf{2}}}=\mathbf{20},\text{ }\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}\] find\[\mathbf{ab}+\mathbf{b}c+\mathbf{ca}\]

    A)  10                               

    B)  \[-\]10

    C)  20                               

    D) \[-\]20

    Correct Answer: B

    Solution :

    (b): \[ab+bc+ca\] \[=\frac{1}{2}\left[ {{\left( a+b+c \right)}^{2}}-{{\left( a+b+c \right)}^{2}} \right]\] \[=\frac{1}{2}\left[ {{0}^{2}}-20 \right]=10\]


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