√2: s, 1€ Q}. Show that K satisfies the following: K, then x₁ + x₂ € K and X₁ X₂ € K. 9. Let K:= {s + (a) If x₁, x₂ (b) If x 0 and x € K, then 1/x € K. (Thus the set K is a sub field of R. With the order inherited from R, the set K is an ordered field that lies between Q and R.)
√2: s, 1€ Q}. Show that K satisfies the following: K, then x₁ + x₂ € K and X₁ X₂ € K. 9. Let K:= {s + (a) If x₁, x₂ (b) If x 0 and x € K, then 1/x € K. (Thus the set K is a sub field of R. With the order inherited from R, the set K is an ordered field that lies between Q and R.)
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:9. Let K = {s+t√2: s, 1 € Q}. Show that K satisfies the following:
(a) If x₁, x₂ € K, then x₁ + x₂ € K and x₁x₂ € K.
(b) If x #0 and x € K, then 1/x € K.
(Thus the set K is a sub field of R. With the order inherited from R, the set K is an ordered field
that lies between Q and R.)
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