What is the solution for an inverse third order equation when solving for X?

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In summary, The conversation is about solving a formula involving a third order inverse equation. The speaker has swapped the axes and is experiencing a decrease in R2. They are seeking a solution for the equation when cast to calculate X and are unsure of where to start due to rusty algebra skills. A potential solution is suggested to multiply the equation by x^3 and use Cardano's method to find the roots.
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cooka111
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I have a question about solving a formula.

I have a set of data which I have fit to an inverse third order equation, if I swap the axes (use X as Y and vise versa), R2 suffers dramatically but I would like to calculate both Y and X values independantly. I am wondering what the solution for the following equation is when cast to calculate X. My algebra is a little rusty and I am not sure where to start.

y = y[tex]_{0}[/tex]+[tex]\frac{a}{x}[/tex]+[tex]\frac{b}{x^{2}}[/tex]+[tex]\frac{c}{x^{3}}[/tex]

Assuming I have values for a,b,c, and yo, how do I solve this for x?
 
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1. What is an inverse third order equation?

An inverse third order equation is a mathematical expression that involves finding the input value (x) that would result in a given output value (y) when the equation is solved. It is called a third order equation because it involves a variable raised to the power of 3, such as x^3. The inverse aspect refers to finding the input value, or x, instead of the output value, or y.

2. How is an inverse third order equation solved?

To solve an inverse third order equation, you first need to rearrange the equation to isolate the variable, usually by dividing both sides by the coefficient of the variable. Then, you can use the inverse operations of exponentiation and/or logarithms to solve for the variable. In some cases, the equation may need to be simplified or factored before solving.

3. What are some real-life applications of inverse third order equations?

Inverse third order equations are commonly used in physics and engineering to model and solve problems related to motion, such as projectile motion. They are also used in economics to determine the relationship between supply and demand, and in chemistry to calculate reaction rates.

4. Are there any limitations to using inverse third order equations?

One limitation of inverse third order equations is that they may not have real solutions in some cases. This means that the input value, or x, may not have a corresponding output value, or y, that makes the equation true. Another limitation is that they can be difficult to solve without the use of a calculator or computer.

5. How can I check if my solution to an inverse third order equation is correct?

You can check your solution by plugging it back into the original equation and seeing if it results in the given output value. You can also graph the equation and see if the coordinates of the solution point lie on the graph. Additionally, you can use a calculator or computer to verify your solution.

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