Question

BRAINLIEST FOR FIRST ANSWER

Answer 1

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