Question

Найдите корни уравнения (2х-1)^2=3х^2-4х+17 Помогите пожалуйста!)

Answer 1

4x^2 - 4x + 1 = 3x^2 - 4x + 17
4x^2 - 3x^2- 4x + 4x = 17-1
x^2 = 16
x = 4

Answer 2

Solving the Equation (2x-1)^2=3x^2-4x+17

To solve the equation *(2x-1)^2=3x^2-4x+17*, we can follow these steps:

1. Expand the left-hand side of the equation. 2. Simplify the equation by combining like terms. 3. Set the equation equal to zero. 4. Solve for *x* using the quadratic formula or factoring.

Step 1: Expand the Left-Hand Side of the Equation

Expanding *(2x-1)^2* gives us: *(2x-1)^2 = (2x-1)(2x-1) = 4x^2 - 2x - 2x + 1 = 4x^2 - 4x + 1*

Step 2: Simplify the Equation by Combining Like Terms

The equation becomes: *4x^2 - 4x + 1 = 3x^2 - 4x + 17*

Step 3: Set the Equation Equal to Zero

By rearranging the terms, we get: *4x^2 - 3x^2 - 4x + 4x + 1 - 17 = 0* * x^2 - 16 = 0*

Step 4: Solve for x

We can solve the quadratic equation *x^2 - 16 = 0* by factoring: *(x - 4)(x + 4) = 0*

So, the solutions for *x* are: x = 4 and x = -4.

Therefore, the roots of the equation *(2x-1)^2=3x^2-4x+17* are x = 4 and x = -4.

[[6 #]]