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

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The discussion focuses on the transformation of the equation e^y + e^-y = 2x into the quadratic form e^(2y) - 2xe^y + 1 = 0. Participants emphasize the importance of recognizing the relationship between e^y and e^(2y) to facilitate this conversion. The key insight is that by manipulating the first equation, one can derive the second equation through algebraic substitution and recognition of exponential identities. Clarification on notation is also provided, distinguishing between e^(2y) and (e^2)y.

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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

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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