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2 Prove that it a) = (a+b) = (- 1/(-a)= -( - عاها - (a+b) = (- (-a7²b) + (a+b))

2 Prove that it a) = (a+b) = (- 1/(-a)= -( - عاها - (a+b) = (- (-a7²b) + (a+b))

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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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.
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.
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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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