Finding the Solution to a+b*x+x^(-y)+c*x^(-2y)+d*x^(1-2y)=0

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The equation a + b*x + x^(-y) + c*x^(-2y) + d*x^(1-2y) = 0 is discussed as a potential polynomial or transcendental equation depending on the nature of y. If y is an integer, it behaves as a polynomial in x, while a, b, c, and d are functions of another variable, z. The original poster seeks a solution for x, ideally in a neat algebraic form, but numerical methods have yielded inconsistent results. Participants suggest that while specific values of y might allow for a solution, a general algebraic solution is unlikely. The discussion emphasizes the complexity of the equation and the challenges in finding a definitive solution.
natski
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Does anyone know how you would go about solving:

a + b*x + x^(-y) + c*x^(-2y) + d*x^(1-2y)=0

solving for x?
 
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can you give more information, on whad do a, b, c, d, x and y represent. Are some of them variables,functions, series, or merely constants?
maybe this information would be helpful to me, and to others also who have more expertise.
 
natski said:
Does anyone know how you would go about solving:

a + b*x + x^(-y) + c*x^(-2y) + d*x^(1-2y)=0

solving for x?

Sure. It's real easy.

a = -b*x - x^(-y) - c*x^(-2y) - d*x^(1-2y)

If that's not the answer you were expecting then how about specifying which variable you want to solve for.
 
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I think he did.

From OP

natski said:
solving for x?
 
natski said:
Does anyone know how you would go about solving:

a + b*x + x^(-y) + c*x^(-2y) + d*x^(1-2y)=0

solving for x?

i guess natski already stated that he wants to solve for x.
 
solving for x?

Whoops, that will teach me to read all of the post and not skip the last line.

Sorry, that'ss a transcendental equation in x, so there will be no closed form solution.
 
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ej uart how do u determine wheather it is transcendental equation in x?
 
sutupidmath said:
ej uart how do u determine wheather it is transcendental equation in x?

Oh yeah it's not transcendental in x. If y is an integer it's a polynomial in x.
 
Um well y is a constant but a,b,c,d are functions of say z. So I want x=function of z or a function of a,b,c,d in this case. I tried to solve numerically for lots of different values of z, plot it and then fit a function to the plot. This worked except for my answer didn't agree with what it should. So I was hoping for a neater algebraic solution.
 
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So I was hoping for a neater algebraic solution.

Well there might be some partiucular values of "y" for which it can work, but in general I don't think it's going to be possible.
 
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