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Prove by contradiction. If a and b are rational numbers, b ≠ 0, and r is an irrational number, then a + br is irrational

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.1: The Field Of Real Numbers

Problem 19E: Prove that if is a nonzero rational number and is irrational, then is irrational.

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Prove by contradiction.

If a and b are rational numbers, b ≠ 0, and r is an irrational

number, then a + br is irrational

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