Thread: Fields

let a= cuberoot(2+sqrt(6)), what does the field Q(a) look like?
If B=a^2 +a +2, then express B^-1 in the form alpha_5(a^5)+ alpha_4(a^4)+...+alpha_0 where the alpha_i's exist in Q.

Originally Posted by Coda202

let a= cuberoot(2+sqrt(6)), what does the field Q(a) look like?
If B=a^2 +a +2, then express B^-1 in the form alpha_5(a^5)+ alpha_4(a^4)+...+alpha_0 where the alpha_i's exist in Q.

If then so . Thus, is root of polynomial . This polynomial is irreducible so are all elements of form for .