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)?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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