Find c_1,c_2,c_3 in QQ such that (1+alpha^4)−1=c_1+c_2 alpha+c_3 alpha^2 in QQ(alpha).

owsicag7 2022-07-15 Answered
Find c 1 , c 2 , c 3 Q such that ( 1 + α 4 ) 1 = c 1 + c 2 α + c 3 α 2
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Answers (1)

Brenton Gay
Answered 2022-07-16 Author has 13 answers
Write β = 1 + α 4 as a linear combination of 1, α, α 2 using that α 3 = 1 α
Consider the map x β x. Write the matrix of this map with respect to the basis 1, α, α 2
Find the inverse matrix and apply to ( 1 , 0 , 0 ) to find β as a linear combination of 1, α, α 2

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