show that if √a+√b ≠ 0, then ℚ(√a+√b ) = ℚ(√a,√b ) for all a and b in ℚ. [Hint: Compute (a - b) / ℚ(√a+√b ).] [Exercise 27 - Prove in detail that ℚ(√3+√7) = ℚ(√3,√7).] I have exercise 27 completed...how would I generalize this?
show that if √a+√b ≠ 0, then ℚ(√a+√b ) = ℚ(√a,√b ) for all a and b in ℚ. [Hint: Compute (a - b) / ℚ(√a+√b ).] [Exercise 27 - Prove in detail that ℚ(√3+√7) = ℚ(√3,√7).] I have exercise 27 completed...how would I generalize this?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 13E
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Section 31 #28 - Generalizing Exercise 27, show that if √a+√b ≠ 0, then ℚ(√a+√b ) = ℚ(√a,√b ) for all a and b in ℚ.
[Hint: Compute (a - b) / ℚ(√a+√b ).]
[Exercise 27 - Prove in detail that ℚ(√3+√7) = ℚ(√3,√7).]
I have exercise 27 completed...how would I generalize this?
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