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    Question

    If a 3  + b 3  + c 3  =

    62, abc = -6 and (a + b + c) = 5, then what is the value of ab + bc + ac?
    A 6 Correct Answer Incorrect Answer
    B 7 Correct Answer Incorrect Answer
    C 5 Correct Answer Incorrect Answer
    D 3 Correct Answer Incorrect Answer

    Solution

    We know, (a + b + c) 2  = a 2  + b 2  + c 2  + 2ab + 2bc + 2ac

    5 2  = a 2  + b 2  + c 2  + 2(ab + bc + ac)

    a 2  + b 2  + c 2  = 25 - 2(ab + bc + ac))...(i)

    a 3  + b 3  + c 3  = (a + b + c)(a 2  + b 2  + c 2  - ab - bc - ac) + 3abc

    62 = 5 * (25 - 2(ab + bc + ac) - (ab + bc + ac)) + 3 * (-6) (from (i))

    ab + bc + ac = 3

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