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

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Discussion Overview

The discussion centers around the equation a + b*x + x^(-y) + c*x^(-2y) + d*x^(1-2y)=0, specifically focusing on methods for solving for the variable x. Participants explore the nature of the equation, the roles of the variables and constants involved, and the possibility of finding an algebraic solution.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants inquire about the definitions of the variables a, b, c, d, x, and y, suggesting that understanding their roles could clarify the problem.
  • One participant rephrases the equation to isolate a, indicating a potential misunderstanding of the original request to solve for x.
  • A participant asserts that the equation is a transcendental equation in x, while another later challenges this by stating that if y is an integer, the equation becomes polynomial in x.
  • Another participant mentions that a, b, c, and d are functions of another variable z, and expresses difficulty in obtaining a satisfactory numerical solution, seeking a more elegant algebraic approach.
  • It is suggested that certain specific values of y might allow for a solution, but generally, it is believed that an algebraic solution may not be feasible.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the equation, with some asserting it is transcendental while others argue it can be polynomial under specific conditions. There is no consensus on the possibility of finding an algebraic solution.

Contextual Notes

Participants note the dependence on the nature of y (whether it is an integer or not) and the roles of the other variables as functions of z, which may affect the solvability of the equation.

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.
 
Last edited:
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.
 
Last edited:
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.
 
  • #10
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.
 
Last edited:

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