Question

Х^5-х^4-2х^3+2х^2-3х+3=0 как это решить?

Answer 1

$x^5-x^4-2x^3+2x^2-3x+3=0\\(x^5-x^4)-(2x^3-2x^2)-(3x-3)=0\\x^4(x-1)-2x^2(x-1)-3(x-1)=0\\(x-1)(x^4-2x^2-3)=0\\\\x_1-1=0\\x_1=1\\\\x^4-2x^2-3=0|t=x^2\\t^2-2t-3=0\\t_1=-1\\t_2=3\\\\x^2 \neq -1\\x^2=3\\x_{2,3}=б \sqrt{3}$

Ответ: 1; -√3; √3

Answer 2

Solving the Equation х^5-х^4-2х^3+2х^2-3х+3=0

To solve the equation х^5-х^4-2х^3+2х^2-3х+3=0, we can use various methods such as factoring, the rational root theorem, or numerical methods. Let's explore the solution using the given search results.

The equation is a polynomial equation of degree 5, and finding its exact roots can be complex. However, we can attempt to find approximate solutions using numerical methods or factorization.

Using Numerical Methods

One approach to solving this equation is to use numerical methods such as the Newton-Raphson method or the bisection method to find approximate solutions. These methods involve iteratively refining a guess for the root of the equation until a satisfactory approximation is obtained.

Factoring the Equation

Another approach is to attempt to factor the polynomial equation to find its roots. Factoring a polynomial of degree 5 can be challenging, but it may provide insight into the nature of the roots.

Conclusion

In conclusion, the equation х^5-х^4-2х^3+2х^2-3х+3=0 is a polynomial equation of degree 5, and finding its exact roots can be challenging. Numerical methods and factoring are potential approaches to finding approximate solutions. Further analysis or specific constraints on the values of x may be necessary to obtain a more precise solution.

Let me know if you'd like to explore any specific method in more detail!