Here is the question and the proof.
I cannot understand why in the final step we have $[F(x):E]\le [F(x):F(f(x))]$. Is that the fact that we have a tower $F(x)/E/F(f(x))$? But if that is true, how can I see that? Thanks for any help!
2026-04-25 09:00:30.1777107630
(From Milne's notes) Prove that $F(x^2)\cap F(x^2-x)=F$
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