Answer:
is easily seen that a sum of two algebraic numbers αα and ββ is algebraic since one has:
Q(α+β)⊆Q(α,β).
Q(α+β)⊆Q(α,β).
Hence, Q(α+β)Q(α+β) is finite-dimensional since Q(α,β)=Q(α)(β)Q(α,β)=Q(α)(β) is, indeed recall that:
[Q(α,β):Q]=[Q(α,β):Q(α)][Q(α):Q].
[Q(α,β):Q]=[Q(α,β):Q(α)][Q(α):Q].
If pp is an annihilator polynomial of αα and qq one of ββ, then resY(p(Y),q(X−Y))resY(p(Y),q(X−Y)) is an annihilator polynomial of α+βα+β.
In your case, use p=X2−2p=X2−2 and q=X3−5q=X3−5 to find that X6−6X4−10X3+12X2−60X+17X6−6X4−10X3+12X2−60X+17 is an annihilator polynomial of
Explanation:
found this one someone elses genius but i was the first answer
