7. Suppose a1, a2,...,an are integers, r is a solution to the equation x" + a1x"- + a2x"- +.. + an = 0. Prove that ifr is rational, then it is an integer.
7. Suppose a1, a2,...,an are integers, r is a solution to the equation x" + a1x"- + a2x"- +.. + an = 0. Prove that ifr is rational, then it is an integer.
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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Transcribed Image Text:7. Suppose a1, a2,...,an are integers, r is a solution to the equation
x" + a1x"-1 + a2x"-2 +.. + am = 0.
Prove that if r is rational, then it is an integer.
8. Prove that for every n > 1, the sum
1 +
1
+
+ ...
n
is not an integer.
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