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A. Let a be an irrational number and r a nonzero rational number. Prove that if s is a real number, then ar + s orar - s is irrational. B. A Pythagorean triple is a triple of three positive integers a, b, and c such that a² + b² = c². Prove that there is no Pythagorean triple where a, b, and c are all odd.

A. Let a be an irrational number and r a nonzero rational number. Prove that if s is a real number, then ar + s orar - s is irrational. B. A Pythagorean triple is a triple of three positive integers a, b, and c such that a² + b² = c². Prove that there is no Pythagorean triple where a, b, and c are all odd.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve this two part discrete math question

A. Leta be an irrational number and r a nonzero rational number. Prove that if s is a real number, then ar + sor ar - sis irrational. B. A Pythagorean triple is a triple of three positive integers a, b, and c such that a² + b² = c². Prove that there is no Pythagorean triple where a, b, and c are all odd.
Transcribed Image Text:A. Leta be an irrational number and r a nonzero rational number. Prove that if s is a real number, then ar + sor ar - sis irrational. B. A Pythagorean triple is a triple of three positive integers a, b, and c such that a² + b² = c². Prove that there is no Pythagorean triple where a, b, and c are all odd.
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