w is an imaginary root of unity. Prove that (i) (a+ba+ca²)³ + (a+ba² +ca)³ = (2a-b-c) (2b-a-c) (2c-a-b). (ii) If a+b+c= 0, then prove that (a+ba+ca²)³ + (a+ba+ca)³ = 27abc.
w is an imaginary root of unity. Prove that (i) (a+ba+ca²)³ + (a+ba² +ca)³ = (2a-b-c) (2b-a-c) (2c-a-b). (ii) If a+b+c= 0, then prove that (a+ba+ca²)³ + (a+ba+ca)³ = 27abc.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.4: Graphs Of Quadratic Equations: The Discriminant
Problem 20WE
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