 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-1/18i/b/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

False. Take

K = Q, qq u a d L = Q (2), qq u a d M = Q (42) .

Each of

L / K

and

M / L

is a quadratic extension and hence normal. However,

T^{4} - 2

has the root

42

M

while its roots

i 42

and

- i 42

are absent. Thus

M / K

is not normal.

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