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SSC Sample Paper SSC CHSL (10+2) Sample Test Paper-21

  • question_answer
    If \[a+b+c=16\] and \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=154,\]then find the value of\[\left( ab+bc+ac \right).\].

    A)  53                               

    B)  52

    C)  51                               

    D)  54

    Correct Answer: C

    Solution :

      \[a+b+c=16\Rightarrow {{a}^{2}}+{{b}^{2}}+{{c}^{2}}=154\] \[\therefore \,\,{{(a+b+c)}^{2}}={{(16)}^{2}}\] \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2(ab+bc+ca)=256\] \[2(ab+bc+ca)=256-154\] \[ab+bc+ac=\underline{\mathbf{51}}\]


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