Question

Решить уравнение x^3-3x^2+2=0 помогите пожалуйста !!!

Answer 1

Не сложно заметить, что один из корней этого уравнения 1.
1³-3·1²+2=3-3=0
Поэтому вынесем (x-1) за скобки.
Вложение(в нём я делил многочлен на многочлен)
(x-1)(x²-2x-2)=0 (выражение равно нулю. когда хотя бы один из множителей равен нулю)
x-1=0
x=1

$x^2-2x-2=0\\D=4+8=12\\\sqrt{D}=2\sqrt{3}\\x_1=\frac{2-2\sqrt{3}}{2}=1-\sqrt{3}\\x_2=\frac{2+2\sqrt{3}}{2}=1+\sqrt{3}$

Answer 2

Solving the Equation x^3 - 3x^2 + 2 = 0

To solve the equation x^3 - 3x^2 + 2 = 0, we can use the factorization method to find the roots of the equation.

The given equation is x^3 - 3x^2 + 2 = 0.

We can factorize this equation as follows: x^3 - 3x^2 + 2 = (x - 1)(x - 1)(x - 2)

So, the roots of the equation are: x = 1 (with multiplicity 2) and x = 2.

Therefore, the solutions to the equation x^3 - 3x^2 + 2 = 0 are x = 1 (with multiplicity 2) and x = 2.

This information is based on the factorization of the given equation.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.