I don't know how to get equation 4.41 here in the image

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Homework Help Overview

The discussion revolves around deriving equation 4.41 from a set of equations, specifically focusing on the variables A, B, C, D, and E. The context appears to involve algebraic manipulation and possibly linear equations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants suggest various methods for eliminating variables through substitution and manipulation of the equations. There are mentions of solving equations for specific variables and using them in others to simplify the problem. Cramer’s rule is also proposed as a potential method to reduce algebraic complexity.

Discussion Status

The discussion is active, with multiple approaches being explored. Some participants offer specific strategies for manipulating the equations, while others provide alternative methods that may simplify the process. There is no explicit consensus on a single method, indicating a variety of interpretations and potential pathways to the solution.

Contextual Notes

Participants are working under the constraints of the equations provided, specifically referencing equations 4.39 and 4.40, and discussing the implications of eliminating certain variables. The original poster expresses uncertainty about reaching the desired equation, indicating a need for clarification on the process.

Shuvro1994
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Homework Statement
I don't know how to get equation 4.41 here in the image.
Relevant Equations
Please see the image I shared and help me to get equation 4.41 from equation 4.39 and 4.40
15696416050779166116926240560905.jpg
 
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That's a lengthy process. Note that A still appears, so only B,C,D have been eliminated using the four equations. One way to approach this:
Solve the first equation for B, use that in the second equation. Now B is gone. Solve the second equation for C, plug that into the remaining two. Now C is gone as well. Solve one of the last two equations for D, plug it into the other one, solve for E, simplify.
Probably a bit less messy: Solve the first equation for B, use that in the second equation. Write it as ##Ce^{ik_2a}=...## and use that in the other two equations. Solve one of them for ##De^{-ik_2a}=...##, plug it into the other one, and then solve for E.
 
Eq 4.40 is easy to solve for both C and D. Now use Eq 4.39 equation to eliminate B from 4.39(i) equation by putting into 4.39(ii) equation. Now simply put value of C and D in this equation and you will easily get value of E as advertised!
 
Cramer’s rule may help lessen the amount of algebra you need to do.
 

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