
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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27. Prove in detail that Q(V3+ 7) = Q(/3, /7).
28. Generalizing Exercise 27, show that if a + vb 0, then Q(Va + vb) = Q(/a, Vb) for all a and b in Q.
[Hint: Compute (a – b)/(Va+ vb).]
29. Let E be a finite extension of a field F, and let p(x) E F[x] be irreducible over F and have degree that is not
a divisor of [E : F]. Show that p(x) has no zeros in E.
|3|](https://content.bartleby.com/qna-images/question/b4dd8e23-ab66-4b24-8e54-a64daec9031c/74e57569-b528-4e6e-b1fa-88b52bc23036/pdrb0gm_thumbnail.jpeg)
Transcribed Image Text:field.
27. Prove in detail that Q(V3+ 7) = Q(/3, /7).
28. Generalizing Exercise 27, show that if a + vb 0, then Q(Va + vb) = Q(/a, Vb) for all a and b in Q.
[Hint: Compute (a – b)/(Va+ vb).]
29. Let E be a finite extension of a field F, and let p(x) E F[x] be irreducible over F and have degree that is not
a divisor of [E : F]. Show that p(x) has no zeros in E.
|3|
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