Question

2. (2х - 2)²= 3. (3х - 1/2)² = 4. (5х² + 2)² =

Answer 1

Я зрозуміла це: 1/2 як дріб, якщо я зрозуміла не правильно то вибач

Answer 2

To solve each of these equations, we can follow these steps:

1. Expand the squared expressions.
2. Set each expression equal to the given constant.
3. Solve for x.

Let's go through each equation:

1. (2x - 2)² = 3

   Expand the squared expression:

   (2x - 2)² = 4x² - 8x + 4

   Now, set it equal to 3:

   4x² - 8x + 4 = 3

   Subtract 3 from both sides:

   4x² - 8x + 4 - 3 = 0

   Simplify:

   4x² - 8x + 1 = 0

   Now, you can solve this quadratic equation using the quadratic formula:

   x = (-b ± √(b² - 4ac)) / (2a)

   In this case, a = 4, b = -8, and c = 1. Plug these values into the formula:

   x = (-(-8) ± √((-8)² - 4(4)(1))) / (2(4))

   x = (8 ± √(64 - 16)) / 8

   x = (8 ± √48) / 8

   x = (8 ± 4√3) / 8

   Simplify further:

   x = (1 ± √3)/2

2. (3x - 1/2)² = 4

   Expand the squared expression:

   (3x - 1/2)² = 9x² - 3x + 1/4

   Now, set it equal to 4:

   9x² - 3x + 1/4 = 4

   Subtract 4 from both sides:

   9x² - 3x + 1/4 - 4 = 0

   Simplify:

   9x² - 3x - 15/4 = 0

   You can solve this quadratic equation using the quadratic formula as in the previous step.

3. (5x² + 2)² = 4

   Expand the squared expression:

   (5x² + 2)² = 25x^4 + 20x² + 4

   Now, set it equal to 4:

   25x^4 + 20x² + 4 = 4

   Subtract 4 from both sides:

   25x^4 + 20x² = 0

   You can factor this equation:

   5x²(5x² + 4) = 0

   Now, set each factor equal to 0:

   1. 5x² = 0 x² = 0 x = 0

   2. 5x² + 4 = 0

   Unfortunately, this equation doesn't have real solutions since the discriminant (4² - 4(5)(0)) is negative, indicating complex solutions.

So, the solutions to the equations are:

1. x = (1 ± √3)/2

2. x = 0

For the third equation, there are no real solutions.