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a+b+c=0 a^3+b^3+c^3=?

a+b+c=0


a^3+b^3+c^3=?

Grade:

1 Answers

Ashtik Mahapatra
30 Points
8 years ago

We use the identity that

a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2 + b^2 + c^2 - ab - bc - ca)

 

Now, if a+b+c = 0, the RHS becomes zero, thus the LHS is also zero

=> a^3 + b^3 + c^3 - 3abc = 0

=> a^3 + b^3 + c^3 = 3abc

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