Question

If a β are not real cube roots of unity, then a^5+ β^5+a β =? (a refers to alpha)

Answer 1

Put:

\[\alpha = w\]
\[\beta = w^2\]

Answer 2

what's the answer?

Answer 3

You tell me..

Answer 4

i don't know...

Answer 5

What 'll be the answer after putting α=w

β=w2

Answer 6

What you don't know tell me..

Answer 7

I dont know the answer of this question.. please tell me if u've solved this?

Answer 8

Firstly put and then show me your work...
do this much only..

Answer 9

ok, wait...

Answer 10

I'm getting the answer 0

Answer 11

You are right if you are getting zero..

Answer 12

If a β are not real cube roots of unity, then we always put α=w and β=w^2?

Answer 13

Yes..

Answer 14

You can put also b=w and a = w^2

That does not matter..

Answer 15

okey then what will be the value of (α^4+β^4) + 1/αβ

Answer 16

You tell me..

Answer 17

i m getting w+w ?

Answer 18

You are wrong..
it is again zero..

Answer 19

oh yes, i forgot to include 1. yup its zero

Answer 20

yes it is..

Answer 21

the shortest trick is to put α and β w and w^2 respectively... Thanks!

Answer 22

FORMULAS TO REMEMBER IN THIS:

\[\huge \color{green}{1 + \omega + \omega^2 = 0}\]

\[\huge \color{blue} {\omega^3 = 1}\]