5. Suppose x is transcendental. Show that if k is a positive integer, then ** is transcendental. (Hint: Suppose x is algebraic and write an equation for xk. Show how this gives an equation for x.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 56E
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5. Suppose x is transcendental. Show that if k is a positive integer, then **
is transcendental. (Hint: Suppose x is algebraic and write an equation for
xk. Show how this gives an equation for a.)
Transcribed Image Text:5. Suppose x is transcendental. Show that if k is a positive integer, then ** is transcendental. (Hint: Suppose x is algebraic and write an equation for xk. Show how this gives an equation for a.)
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