Question
If (x2 + y2 + z2 -
4x + 6y + 13) = 0, then find the value of (x + y + z).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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