Question

Решите уравнение: (3x-1)^2-8(x+1)^2=(x+2)(x-2) Помогите плиииз!

Answer 1

Ответ:
(3x-1)^2-8(x+1)^2=(x+2)(x-2)
9x^2-6x+1-8(x^2+2x+1)=x^2-4
9x^2-6x+1-8x^2-16x-8=x^2-4
x^2-x^2-6x-16x=-4+7
-22x=3
x=-3/22

Answer 2

9х^2-6х+1-8(х^2+2х+1)=х^2 -2х+2х-4
9х^2-6х+1-8х^2-16х-8=х^2-4
-6х-16х=-4-1+8
-22х=3
Х=-3/22

Answer 3

Solving the Equation: (3x-1)^2-8(x+1)^2=(x+2)(x-2)

To solve the equation (3x-1)^2-8(x+1)^2=(x+2)(x-2), we will follow these steps:

Step 1: Expand and simplify the equation. Step 2: Rearrange the equation to bring all terms to one side. Step 3: Factorize the equation. Step 4: Solve for x.

Let's go through each step in detail.

Step 1: Expand and Simplify the Equation

Expanding the equation, we get:

(3x-1)^2 - 8(x+1)^2 = (x+2)(x-2)

Simplifying further, we have:

9x^2 - 6x + 1 - 8(x^2 + 2x + 1) = x^2 - 4

Expanding and simplifying the equation, we get:

9x^2 - 6x + 1 - 8x^2 - 16x - 8 = x^2 - 4

Simplifying further, we have:

x^2 - 22x - 11 = 0

Step 2: Rearrange the Equation

To bring all terms to one side, we rearrange the equation as follows:

x^2 - 22x - 11 = 0

Step 3: Factorize the Equation

To factorize the equation, we need to find two numbers whose product is -11 and whose sum is -22. After some calculation, we find that the numbers are -1 and 11. Therefore, we can factorize the equation as follows:

(x - 1)(x - 11) = 0

Step 4: Solve for x

To solve for x, we set each factor equal to zero and solve for x:

x - 1 = 0 --> x = 1

x - 11 = 0 --> x = 11

Therefore, the solutions to the equation are x = 1 and x = 11.

I hope this helps! Let me know if you have any further questions.