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    Question

    If a, b and c are integers such that a 3  + b

    3  + c 3  = 192 + 3abc, ab + bc + ac = a 2  + b 2  + c 2  - 16, then what is the value of (a + b + c)?
    A 20 Correct Answer Incorrect Answer
    B 12 Correct Answer Incorrect Answer
    C 8 Correct Answer Incorrect Answer
    D 16 Correct Answer Incorrect Answer

    Solution

    As we know, a 3  + b 3  + c 3  = (a + b + c)(a 2  + b 2  + c 2  - ab - bc - ac) + 3abc

    Then, 192 + 3abc = (a + b + c)(a 2  + b 2  + c 2  - (a 2  + b 2  + c 2  - 16)) + 3abc

    a + b + c = 12

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