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Question
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
Options
0
abc
3abc
2abc
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Solution
If a + b + c = 0, then a3 + b3 + c3 is equal to 3abc.
Explanation:
We know that,
a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2 – ab – bc – ca)
As, a + b + c = 0,
So, a3 + b3 + c3 – 3abc = (0) (a2 + b2 + c2 – ab – bc – ca) = 0
Hence, a3 + b3 + c3 = 3abc.
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