Question : a3 + b3 + c3 = 3abc if _________.
Option 1: a = b = c
Option 2: a + b + c = 0
Option 3: a + b + c = 1
Option 4: a + b + c = –1
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Correct Answer: a + b + c = 0
Solution :
We know that a
3
+ b
3
+ c
3
= (a + b + c) (a
2
+ b
2
+ c
2
– ab – bc – ca) + 3abc
So, a
3
+ b
3
+ c
3
= 3abc when (a + b + c) = 0
Hence, the correct answer is (a + b + c) = 0.
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