2 Prove that it a) = (a+b) = (- 1/(-a)= -( - عاها - (a+b) = (- (-a7²b) + (a+b))
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Certainly! Here is the transcription of the content from the image for educational purposes:
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1) Prove that if a > b, then:
a) \((-a \cdot b) = (-a) \cdot (b)\)
b) \((-a \cdot b) = (a) \cdot (-b)\)
Given: \( (a > b) \)
To prove:
\((-a \cdot b) = (-a) \cdot (c - b)\)
- Start with: \((-a \cdot b) + (a \cdot b) = (c - a) \cdot (c - b)\)
- Therefore, \((-a \cdot b) = (a \cdot b) / b / b\)
\[ 0 = 0 \]
(Proof complete)
---
No graphs or diagrams are present in the image. The main focus is on a mathematical proof concerning inequalities and product properties.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7dbb4ae4-0d65-4baa-9481-63f79be91eca%2F637c048a-0162-4e49-b5ee-9608b4e8d934%2F3um4wt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here is the transcription of the content from the image for educational purposes:
---
1) Prove that if a > b, then:
a) \((-a \cdot b) = (-a) \cdot (b)\)
b) \((-a \cdot b) = (a) \cdot (-b)\)
Given: \( (a > b) \)
To prove:
\((-a \cdot b) = (-a) \cdot (c - b)\)
- Start with: \((-a \cdot b) + (a \cdot b) = (c - a) \cdot (c - b)\)
- Therefore, \((-a \cdot b) = (a \cdot b) / b / b\)
\[ 0 = 0 \]
(Proof complete)
---
No graphs or diagrams are present in the image. The main focus is on a mathematical proof concerning inequalities and product properties.
Expert Solution
Step 1: Introduction
To prove these properties, you can use the properties of real numbers and basic algebraic manipulations. Here's how you can prove each of the given statements:
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