Question : If a + b + c = 0, the value of (a3 + b3 + c3) is:
Option 1: abc
Option 2: 2abc
Option 3: 3abc
Option 4: 0
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Correct Answer: 3abc
Solution :
Given: a + b + c = 0
a
3
+ b
3
+ c
3
– 3abc = (a + b + c)(a
2
+ b
2
+ c
2
– ab – bc – ca)
⇒ a
3
+ b
3
+ c
3
– 3abc = (0)(a
2
+ b
2
+ c
2
– ab – bc – ca)
⇒ a
3
+ b
3
+ c
3
– 3abc = 0
⇒ a
3
+ b
3
+ c
3
= 3abc
Hence, the correct answer is 3abc.
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