E^y + e^-y =2x or e^2y - 2xe^y + 1 = 0 equation

  • Context: Undergrad 
  • Thread starter Thread starter thenewbosco
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Discussion Overview

The discussion revolves around the transformation of the equation e^y + e^-y = 2x into the form e^2y - 2xe^y + 1 = 0. Participants are exploring the steps and reasoning behind this mathematical manipulation.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Exploratory

Main Points Raised

  • One participant notes the presence of e^(2y) in the second equation and suggests considering how to manipulate the first equation to introduce this term.
  • Another participant emphasizes the importance of understanding the difference between the two equations and encourages self-discovery of the transformation process.
  • A participant expresses confusion about the transformation and requests further assistance in understanding the steps involved.
  • There is a clarification regarding the notation, with a participant pointing out that e^2y should be interpreted as e raised to the power of 2y, rather than (e^2)y.
  • One participant questions whether hints provided earlier have been utilized in the problem-solving process.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the transformation process, with some expressing confusion and others providing hints or suggestions without resolving the underlying question.

Contextual Notes

There are indications of missing steps in the transformation process, and participants are working with different interpretations of the notation used in the equations.

thenewbosco
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In this textbook i am looking at it says:

"Thus e^y + e^-y =2x or

e^2y - 2xe^y + 1 = 0"

how did they go from the first to the second part?
 
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Well, look at pieces of the equation and see if that gives you any clues.

For example, their second equation has an e^(2y) in it1. Can you think of anything to do to the first equation so that the result will have an e^(2y) in it?

1: I assume you meant e^(2y) and not e^2y (which is the same as (e^2)y)
 
You should really try to figure this out yourself. What's the difference between the two equations?
 
i still don't get how to go from

[tex]e^y + exp(-y)=2x[/tex]

to

[tex]e^2y - 2xe^y + 1 = 0[/tex]

help please
 
I'm not sure, but that y should be raised too...e^(2y) not (e^2)y
 
Have you tried any of our hints?
 

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