Question

x^3-4x^2-x+4=0 пожалуйста решите

Answer 1

x^3-4x^2-x+4=0

x^2(x-4)-1(x-4)=0

(x-4)(x^2-1)=0

x=4

x=1

x=-1

 

 

Answer 2

Solving the Equation x^3 - 4x^2 - x + 4 = 0

To solve the equation x^3 - 4x^2 - x + 4 = 0, we can use various methods such as factoring, the quadratic formula, or synthetic division. Let's proceed with finding the roots of the given equation.

First, let's factor the equation and then solve for the roots.

The given equation is: x^3 - 4x^2 - x + 4 = 0

To factor the equation, we can use different methods such as the rational root theorem, grouping, or synthetic division. Let's proceed with factoring the equation.

Factoring the equation: x^3 - 4x^2 - x + 4 = 0

We can factor the equation as: (x - 2)(x^2 - 2x - 2) = 0

Now, we have factored the equation into two parts: 1. x - 2 = 0 2. x^2 - 2x - 2 = 0

Let's solve for the roots of each part.

Solving x - 2 = 0

The solution for x - 2 = 0 is: x = 2

Solving x^2 - 2x - 2 = 0

To solve the quadratic equation x^2 - 2x - 2 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 1, b = -2, and c = -2.

Using the quadratic formula, we get: x = (2 ± √(2^2 - 4*1*(-2))) / (2*1) x = (2 ± √(4 + 8)) / 2 x = (2 ± √12) / 2 x = (2 ± 2√3) / 2 x = 1 ± √3

So, the solutions for x^2 - 2x - 2 = 0 are: x = 1 + √3 and x = 1 - √3

Therefore, the solutions for the given equation x^3 - 4x^2 - x + 4 = 0 are: x = 2, x = 1 + √3, and x = 1 - √3.

This completes the solution for the given equation.