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

  • Thread starter natski
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In summary, the conversation is about solving the equation a + b*x + x^(-y) + c*x^(-2y) + d*x^(1-2y)=0 for the variable x. The participants discuss the variables a, b, c, d, x, and y and their representations in the equation. They also consider different methods of solving the equation, including solving it numerically and fitting a function to a plot. However, it is determined that the equation is a transcendental equation in x and it is unlikely to have a neat algebraic solution.
  • #1
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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  • #2
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.
 
  • #3
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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  • #4
I think he did.

From OP

natski said:
solving for x?
 
  • #5
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.
 
  • #6
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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  • #7
ej uart how do u determine wheather it is transcendental equation in x?
 
  • #8
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.
 
  • #9
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.
 
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1. What is the equation trying to solve?

The equation is trying to find the value of x that makes the entire expression equal to zero.

2. How do I solve this equation?

This equation can be solved using algebraic techniques, such as factoring or using the quadratic formula.

3. Can this equation have more than one solution?

Yes, this equation can have multiple solutions for x depending on the values of a, b, c, and d.

4. What are the variables in this equation?

The variables in this equation are x and y. The constants are a, b, c, and d.

5. What is the importance of finding the solution to this equation?

Finding the solution to this equation can help solve real-world problems and can also provide insights and understanding in mathematics and science.

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