Given x + y + z = 0, and x3 + y3 + z3 = 3xyz, evaluate (x - y)3 + (y - z)3 + (z - x)3.
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 3(x - y)(y - z)(z - x).
Let a = x – y, b = y – z, c = z – x
Here, (x – y) + (y – z) + (z – x) = 0
So, a + b + c = 0, then a3 + b3 + c3 = 3abc
(x – y)3 + (y – z)3 + (z – x)3 = 3(x – y)(y – z)(z – x)