Question

4х^2 - 3х = 3(12 - х) ? х^2 - 3х = 2( 12 -х ) - х ? -х^2 +6х = 2( 12 + 2х) +2х ?

Answer 1

1. 4х² - 3х = 3 ( 12 - х )
4х² - 3х = 36 - 3х
4х² - 3х + 3х = 36
4х² = 36
х² = 9
х = ±3.
Ответ : х = ±3.

2. х² - 3х = 2 ( 12 - х ) - х
х² - 3х = 24 - 2х - х
х² - 3х + 2х + х = 24
х² = 24
х = ± √24.
Ответ : х = ± √24.

3. -х² + 6х = 2 ( 12 + 2х ) + 2х
-х² + 6х = 24 + 4х + 2х
-х² + 6х - 4х - 2х = 24
-х² = 24
х² = -24.
Ответ : нет решений.
Нет решений, так как нет такого числа, квадрат которого равен отрицательному числу.

Удачи))))

Answer 2

To solve each of these equations, we'll start by simplifying them step by step.

1. 4x^2 - 3x = 3(12 - x)

Step 1: Distribute the 3 on the right side. 4x^2 - 3x = 36 - 3x

Step 2: Move all terms to one side to set the equation to 0. 4x^2 - 3x - 36 + 3x = 0

Step 3: Combine like terms. 4x^2 - 36 = 0

Step 4: Factor the quadratic equation, if possible. 4(x^2 - 9) = 0

Step 5: Set each factor to zero and solve for x. x^2 - 9 = 0 x^2 = 9 x = ±√9 x = ±3

So, the solutions for the first equation are x = 3 and x = -3.

2. x^2 - 3x = 2(12 - x) - x

Step 1: Distribute the 2 on the right side. x^2 - 3x = 24 - 2x - x

Step 2: Move all terms to one side to set the equation to 0. x^2 - 3x + 2x + x - 24 = 0

Step 3: Combine like terms. x^2 = 0

Step 4: Solve for x. x = 0

The solution for the second equation is x = 0.

3. -x^2 + 6x = 2(12 + 2x) + 2x

Step 1: Distribute the 2 on the right side. -x^2 + 6x = 24 + 4x + 2x

Step 2: Move all terms to one side to set the equation to 0. -x^2 + 6x - 4x - 2x - 24 = 0

Step 3: Combine like terms. -x^2 = 0

Step 4: Solve for x. x^2 = 0

Since both sides are equal to 0, the equation is true for all real values of x. The solution for the third equation is x can be any real number.