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a. Prove that √6 is irrational. b. There exist no integers a and b for which 21a+30b=1. c. If a and b are positive real numbers, then a+b>2ab. d.Suppose a,bEZ. If 4| (a^2+b^2), then a and b are not both odd.

a. Prove that √6 is irrational. b. There exist no integers a and b for which 21a+30b=1. c. If a and b are positive real numbers, then a+b>2ab. d.Suppose a,bEZ. If 4| (a^2+b^2), then a and b are not both 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
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Use the method of proof by contradiction to prove the following statement. (In each case, think about how a direct or contrapositive proof would work. In most cases proof by contradiction is easier a. Prove that √6 is irrational. b. There exist no integers a and b for which 21a+30b=1. c. If a and b are positive real numbers, then a+b>2ab. d. Suppose a, beZ. If 4| (a^2+b^2), then a and b are not both odd.
Transcribed Image Text:Use the method of proof by contradiction to prove the following statement. (In each case, think about how a direct or contrapositive proof would work. In most cases proof by contradiction is easier a. Prove that √6 is irrational. b. There exist no integers a and b for which 21a+30b=1. c. If a and b are positive real numbers, then a+b>2ab. d. Suppose a, beZ. If 4| (a^2+b^2), then a and b are not both odd.
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