Can x be found for ax^b - x^(b-2) = c in the general form?

In summary, the equation ax^b - x^(b-2) = c is a general form where a and b are constants and x is the variable. It can be solved for x using algebraic techniques and has a degree of b. It can have a maximum of b solutions, depending on the values of a, b, and c, and can also have no real solutions. This equation can also be graphed on a Cartesian plane, with the number of solutions determined by counting the intersections with the x-axis.
  • #1
Superposed_Cat
388
5
I have an long equation I managed to simplify to that form, but now I haven't the foggiest on how to solve for x, any help appreciated
 
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  • #2
Not in a closed form. There might be some way with infinite fractions or similar approaches.
 
  • #3
Only if ##b\le 4##.
 
  • #4
... and ##b \geq -2## and an integer.

Or c=0 or a=0, but none of these special cases help with the general problem.
 

Related to Can x be found for ax^b - x^(b-2) = c in the general form?

1. Can you explain the general form of the equation ax^b - x^(b-2) = c?

The general form of this equation is a polynomial equation in the form of ax^b - x^(b-2) = c, where a and b are constants and x is the variable. This equation is also known as a power function, where the variable x is raised to a power (b) and multiplied by a constant (a), and then the result is subtracted by the variable x raised to a power (b-2).

2. What is the purpose of finding x in this equation?

The purpose of finding x in this equation is to determine the value of the variable that satisfies the given equation. This can help in solving real-world problems or in understanding the behavior of functions.

3. Is it possible to find an exact value for x in this equation?

In some cases, it is possible to find an exact value for x in this equation. However, there are also cases where only an approximate value can be found using numerical methods. It depends on the values of a, b, and c in the equation.

4. What are the common methods used to solve this equation?

The common methods used to solve this equation include factoring, using the quadratic formula, and using numerical methods such as Newton's method or the bisection method. The method used may vary depending on the values of a, b, and c in the equation.

5. Can this equation be solved for any values of a, b, and c?

Yes, this equation can be solved for any values of a, b, and c. However, the methods used to solve it may vary depending on the values of these constants. In some cases, the equation may not have a solution or may have an infinite number of solutions.

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