Exams › SSC CGL (Prelims) › General

Given that a + b + c = 0 and a^3 + b^3 + c^3 = 3abc, find the value of (a - b)^3 + (b - c)^3 + (c - a)^3.

1. 0
2. 9(a - b)(b - c)(c - a)
3. 27abc
4. 3(a - b)(b - c)(c - a)

Correct answer: 3(a - b)(b - c)(c - a)

Solution

Set x = a-b, y = b-c, z = c-a. Their sum is zero, so by the identity x^3 + y^3 + z^3 = 3xyz. Substituting back gives 3(a-b)(b-c)(c-a).

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