If a+b+c=0

Then find the value of a³+b³+c³

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Solution

We know from the identity,
a³+b³ + c³ = (a+ b + c) (a² + b² + c² – ab – be – ca) + 3abc

i.e.
a³+b³ + c³ – 3 abc = (a + b + c)(a²+b²+c²–ab–bc-ca)
[∴ a + b + c = 0]

a³+b³ + c^{3 –}3abc = 0

So
a³+b³+c³=3abc

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