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(a) Using Proposition 1.3.2 and/or the definition of absolute value, prove that if b ‡ 0, 1 1|2|= |b|` then (b) Prove that for all a E R and b = 0, we have |a| |b| a .

(a) Using Proposition 1.3.2 and/or the definition of absolute value, prove that if b ‡ 0, 1 1|2|= |b|` then (b) Prove that for all a E R and b = 0, we have |a| |b| a .

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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proposition 1.3.2 ( 

Proposition 1.3.2. For any two real numbers x, y, we have √₁² = |x| |x|² = x² 2 x ≤ |x| and |x · y| = |x|·|y|.
Transcribed Image Text:Proposition 1.3.2. For any two real numbers x, y, we have √₁² = |x| |x|² = x² 2 x ≤ |x| and |x · y| = |x|·|y|.
(a) Using Proposition 1.3.2 and/or the definition of absolute value, prove that if b = 0, 1 then | - |b| (b) Prove that for all a E R and b = 0, we have b a b - |b|
Transcribed Image Text:(a) Using Proposition 1.3.2 and/or the definition of absolute value, prove that if b = 0, 1 then | - |b| (b) Prove that for all a E R and b = 0, we have b a b - |b|
Expert Solution
Step 1

The proposition is given by :  For any two real numbers  x and y  we have 

     x2=x ,  x2=x2  ,  x≤x   and  x·y=x·y

We have to prove that ,

a   if b≠0, then  1b=1bb  for all a∈ℝ and b≠0 , we have   ab=ab

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