If a + b + c = 0, then write the value of a³+b³+c³.
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Given : a + b + c = 0.
To find : The value of a³ + b³ + c³.
We have, a + b + c = 0
We know that if, a + b + c = 0, then a³ + b³ + c³ = 3abc
Hence, the value of a³ + b³ + c³ is 3abc.
Extra information :
We know that, a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c²− ab − bc − ca)
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We know that:
When a + b + c = 0,
a³ + b³ + c³ = 3abc
Alternative:
The identity states:
a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ac)
When a + b + c = 0
=> a³ + b³ + c³ = 3abc
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