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Xy - X. y X*5 lay substitution x ky algebra why 8970? a IS by algebre to? qa are botth integers and the since '^ P, b, e and b e integers are closed under

Xy - X. y X*5 lay substitution x ky algebra why 8970? a IS by algebre to? qa are botth integers and the since '^ P, b, e and b e integers are closed under

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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Can you help prove qa is not equal 0 before I can x is rational.
9:47 4 (3. het S be the statemout: The product of irrational mumber and any rational number any non zero is icrational. a) write a negetion for S: There exists an irrational munber nd a rational mumber non 7ere ratonal. whose productis b) Prove S bu contraction : Suppose not and Then there exists an irrational x rational number y such that 스 non zero the pnduct of x.u is vatunal. Then Let and with for some integers a,b, P and ky detinitian of rational. Xy - X. y - X. * ay substitution b - x ky algebra IS a why Pb. by algebre Now pb and qa are both integers A P,b, q and and the Since, are integers bese integers are closed undr products. X is ratlanal which contradict * is irratiomal .There fore the fact that the a ssumption was wrony and X is irrational.
Transcribed Image Text:9:47 4 (3. het S be the statemout: The product of irrational mumber and any rational number any non zero is icrational. a) write a negetion for S: There exists an irrational munber nd a rational mumber non 7ere ratonal. whose productis b) Prove S bu contraction : Suppose not and Then there exists an irrational x rational number y such that 스 non zero the pnduct of x.u is vatunal. Then Let and with for some integers a,b, P and ky detinitian of rational. Xy - X. y - X. * ay substitution b - x ky algebra IS a why Pb. by algebre Now pb and qa are both integers A P,b, q and and the Since, are integers bese integers are closed undr products. X is ratlanal which contradict * is irratiomal .There fore the fact that the a ssumption was wrony and X is irrational.
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