Solving an Odd Equation: Two Different x Values for Same F?

[eahaidar]

Hello everyone
I want to solve this equation
F(x)=Ax/((bx*x)+c =constant which is an odd function in which we get same positive and negative solutions for each F
But If I solve his equation I get two different x values for The same F any suggestions??
Thank you

 

[Mark44]

Hello everyone
I want to solve this equation
F(x)=Ax/((bx*x)+c =constant which is an odd function in which we get same positive and negative solutions for each F
But If I solve his equation I get two different x values for The same F any suggestions??

Do you mean two different x values for the same value of what you're calling the constant?

Graph y = x/(x^2 + 1) to get an idea of what your function F looks like.

 

[eahaidar]

First thank you for the reply
Second yes these are all constants but what I am asking about is how come if I solve it analytically I would not get 2 values on x same but opposite to each other
But different values of x

 

[Simon Bridge]

yes these are all constants

... surely you are treating x as a variable?
You seem to be wanting to solve: $$a=\frac{x}{bx^2+c}$$... here a=<constant>/A which is also a constant.

This becomes $abx^2-x+ac = 0$ which is a quadratic equation.

You are getting two possible values of x for given values of a,b, and c because there are two possible values that make the relation true. What is the problem?

Your concern seems to be that you are getting $\pm$ <the same number> as the roots ... if so, then please show your working.

 

[CellCoree]

for sharing your equation with us! It seems like you have come across an interesting problem in your equation. In mathematics, it is not uncommon for an equation to have multiple solutions for a given value of the variable. This is especially true for odd functions, where the graph is symmetrical about the origin and crosses the x-axis at multiple points.

In this case, it is possible for the equation to have two different x values that yield the same F value. This is because the symmetry of the function allows for both positive and negative values of x to produce the same output. It is important to note that this does not mean the equation is incorrect or that there is an error in your calculations.

One way to approach this situation is to plot the function and visually analyze the points of intersection with the x-axis. This can help you identify the different x values that yield the same F value. Additionally, you could also consider using a numerical method, such as Newton's method, to find the approximate solutions for your equation.

I hope this helps to clarify the situation. Keep exploring and experimenting with your equation to gain a deeper understanding of its behavior. Good luck!