Prove that (a+b omega+c omega2)3+(a+b omega2+c omega)3=27abc,if a+b+c=0

Question

Complex number. Pllease sir do it in a very .easy school grade (11) ones

Answer 1

Zicon,

 

Please verify that THIS is the problem:

 

Prove: (a + bω + cω²)³ + (a + bω² + cω)³ = 27abc,

Given: a + b + c = 0.

 

(This reminds me of an old Putnam Exam or IMO question from many years ago. Where did you get it?)