Problem 2 Prove that √6 is not a rational number; i.e. there are no integers a, b € Zsuch that √6 = . Notes: • A fraction is in lowest terms if there is no integer k that divides both a and b. • It is traditional in math classes that you can use anything you have previously proven. You might find a problem from the last warmup to be helpful. • It is also traditional that you may "use without proof" facts that the instructor tells you are acceptable to use without proof. In this case, you may use without proof the fact that, for any integer n, it is the case that n² is even if and only if n is even.
Problem 2 Prove that √6 is not a rational number; i.e. there are no integers a, b € Zsuch that √6 = . Notes: • A fraction is in lowest terms if there is no integer k that divides both a and b. • It is traditional in math classes that you can use anything you have previously proven. You might find a problem from the last warmup to be helpful. • It is also traditional that you may "use without proof" facts that the instructor tells you are acceptable to use without proof. In this case, you may use without proof the fact that, for any integer n, it is the case that n² is even if and only if n is even.
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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Transcribed Image Text:Problem 2
Prove that √6 is not a rational number; i.e. there are no integers a, b € Z such that √6 = %.
Notes:
• A fraction is in lowest terms if there is no integer k that divides both a and b.
• It is traditional in math classes that you can use anything you have previously proven. You might find a problem from the last
warmup to be helpful.
• It is also traditional that you may "use without proof" facts that the instructor tells you are acceptable to use without proof. In this
case, you may use without proof the fact that, for any integer n, it is the case that n² is even if and only if n is even.
Problem 3
Prove that if n is an integer, then 3n² +n +4 is even.
Hint: Divide into cases based on whether n is odd or even.
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