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Find all real solutions for \(x\) in \(2(2^x- 1) x^2 + (2^{x^2}-2)x = 2^{x+1} -2 .\) 

I found x = -1, 0, and x = 1 as solutions to this problem, but how do I prove these are the only solutions?
 

 Jun 25, 2020
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Isn't it a 3rd order equation because of: 2^x^2 term? if that is the case, then there are only the 3 solutions you found.

 Jun 25, 2020
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How does the 2^(x^2) term mean that the equation is 3rd order?

bepischrist  Jun 25, 2020

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