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    Question

    If (x - 1) 3  + (y - 2) 3  + (z

    - 3) 3  + 3(x + y - 3)(y + z - 5)(x + z - 4) = 0, then what is the value of (x + y + z)?
    A 8 Correct Answer Incorrect Answer
    B 2 Correct Answer Incorrect Answer
    C 3 Correct Answer Incorrect Answer
    D 6 Correct Answer Incorrect Answer

    Solution

    As we know, (a + b + c) 3  = a 3  + b 3  + c 3  + 3(a + b)(b + c)(a + c)

    Then, here, a = x - 1, b = y - 2 and c = z - 3

    Now, according to the question:

    a 3  + b 3  + c 3  + 3(a + b)(b + c)(a + c) = 0

    So, (a + b + c) 3  = 0

    (a + b + c) = 0

    Then, (x - 1 + y - 2 + z - 3) = 0

    Therefore, (x + y + z) = 6

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