Question

4x-4=(x-1)в квадрате

Answer 1

4x-4=(x-1)²

4x-4=(x-1)(x-1)

4x-4=x²-x-x+1

4x-4=x²-2x+1

4x-4-x²+2x-1=0

-x²+6x-5=0

D=36-4*(-1)*(-5)=36-20=16

x₁=(-6+4)/(-2)=1

x₂=(-6-4)/(-2)=5

Answer 2

To solve the equation (4x - 4) = (x - 1)^2, follow these steps:

Step 1: Expand the right side of the equation (x - 1)^2: (x - 1)^2 = (x - 1)(x - 1) = x^2 - 2x + 1

Step 2: Rewrite the equation with the expanded form: 4x - 4 = x^2 - 2x + 1

Step 3: Move all terms to one side of the equation to set it to zero: x^2 - 2x - 4x + 1 - 4 = 0

Step 4: Combine like terms: x^2 - 6x - 3 = 0

Now, we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = -6, and c = -3. To solve this equation, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values: x = (6 ± √((-6)^2 - 4 * 1 * -3)) / 2 * 1 x = (6 ± √(36 + 12)) / 2 x = (6 ± √48) / 2 x = (6 ± 4√3) / 2

Now, split the equation into two solutions:

1. x = (6 + 4√3) / 2
2. x = (6 - 4√3) / 2

Step 5: Simplify each solution:

1. x = 3 + 2√3
2. x = 3 - 2√3

So, the two solutions to the equation are x = 3 + 2√3 and x = 3 - 2√3.