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.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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w is an imaginary root of unity.
Prove that
(i) (a+ba+ca)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+ba² + cw)³ = 27abc.
Transcribed Image Text:w is an imaginary root of unity. Prove that (i) (a+ba+ca)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+ba² + cw)³ = 27abc.
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