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    Question

    If (x2 + y2 + z2 -

    4x + 6y + 13) = 0, then find the value of (x + y + z).
    A -2 Correct Answer Incorrect Answer
    B 1 Correct Answer Incorrect Answer
    C -1 Correct Answer Incorrect Answer

    Solution

    We can re-write the above expression as:

    x2 - 4x + 4 + y2 + 6y + 9 + z2 = 0

    Or, (x - 2)2 + (y + 3)2 + z2 = 0

    Since, square of a number can never be negative, all (x - 2)2, (y + 3)2 and z2 have to be '0'.

    So, x - 2 = 0

    Or, x = 2

    (y + 3)2 = 0

    And, y = -3

    And, z2 = 0

    Or, z = 0

    So, required value = 2 - 3 + 0 = -1

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