Write Q(sqrt2) for the set described in exercise 3.1 (iii). given a non zero element a + bsqrt(2) of Q(sqrt2), express 1/(a + bsqrt2) in the form c + dsqrt(2), where c,d E Q. Prove that multiplication makes Q(sqrt2) - {0} into a group.
Write Q(sqrt2) for the set described in exercise 3.1 (iii). given a non zero element a + bsqrt(2) of Q(sqrt2), express 1/(a + bsqrt2) in the form c + dsqrt(2), where c,d E Q. Prove that multiplication makes Q(sqrt2) - {0} into a group.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.1: Definition Of A Ring
Problem 20E
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Write Q(sqrt2) for the set described in exercise 3.1 (iii). given a non zero element a + bsqrt(2) of Q(sqrt2), express 1/(a + bsqrt2) in the form c + dsqrt(2), where c,d E Q. Prove that multiplication makes Q(sqrt2) - {0} into a group.
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