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

  • question_answer
    If \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}})=125\] and \[\left( \mathbf{ab}+\mathbf{b}c+\mathbf{ca} \right)=\mathbf{50}\] find the value of \[\left( \mathbf{a}+\mathbf{b}+\mathbf{c} \right)\]

    A)  10                               

    B)  15   

    C)  \[\sqrt{15}\]                             

    D)  12

    Correct Answer: B

    Solution :

    (b): \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=125\]               ......1 \[ab+bc+ca=50\]                      ......2 From \[1+2\times 2\] \[\Rightarrow {{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2\left\{ ab+bc+ca \right\}=125+2\times 50\]\[\Rightarrow {{\left( a+b+c \right)}^{2}}=225\] \[\Rightarrow a+b+c=15\]


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