 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-1/20g/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

One has

α^{2} = 4 + 17 \in K

and

N_{K / Q} (α^{2}) = (4 + 17) (4 - 17) = - 1.

α

belonged to

K

, multiplicativity would give

N_{K / Q} (α)^{2} = - 1,

which is impossible because

N_{K / Q} (α) \in Q

. Therefore

α \in / K

and

[L : K] = 2

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