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

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The discussion centers on the transformation of the equation e^y + e^-y = 2x into e^(2y) - 2xe^y + 1 = 0. Participants are encouraged to analyze the components of the first equation to identify how to introduce e^(2y). Clarifications are made regarding the notation, emphasizing that e^(2y) is distinct from (e^2)y. The conversation highlights the importance of understanding the relationships between the terms to facilitate the conversion. Overall, the thread seeks to clarify the mathematical steps involved in this transformation.
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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

e^y + exp(-y)=2x

to

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

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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