Question

3(x - 2)² = 3; уравнение​

Answer 1

Ответ:

1; 3.

Объяснение:

3(x - 2)² = 3

(x - 2)² = 3 : 3

(x - 2)² = 1

х - 2 = 1 или х - 2 = -1

1) х - 2 = 1

х = 2 + 1

х = 3;

2) х - 2 = -1

х = - 1 + 2

х = 1.

Ответ: 1; 3.

Answer 2

To solve the equation 3(x - 2)² = 3, we can follow these steps:

Step 1: Expand the square

3(x - 2)² = 3 3(x - 2)(x - 2) = 3 3(x² - 4x + 4) = 3 3x² - 12x + 12 = 3

Step 2: Simplify the equation

3x² - 12x + 12 - 3 = 0 3x² - 12x + 9 = 0

Step 3: Divide through by 3 to simplify the equation further

x² - 4x + 3 = 0

Step 4: Factorize the equation

(x - 3)(x - 1) = 0

Step 5: Set each factor equal to zero and solve for x

x - 3 = 0 or x - 1 = 0

Solving each equation separately:

For x - 3 = 0: x = 3

For x - 1 = 0: x = 1

So, the solutions to the equation 3(x - 2)² = 3 are x = 3 and x = 1.