Question

РЕШИТЕ (x-2)^2=3(x-2)

Answer 1

${(x - 2)}^{2} = 3 \times (x - 2) \\ {x}^{2} - 4x + 4 = 3x - 6 \\ {x}^{2} - 4x - 3x + 4 + 6 = 0 \\ {x}^{2} - 7x + 10 = 0 \\ a = 1 \\ b = - 7 \\ c = 10 \\ d = { - (b)}^{2} - 4 \times a \times c = - 49 - 40 = - 89 \\ x 1= \frac{ 7 + \sqrt{89}}{2} = 3.5 + \sqrt{89} \\ x2 = \frac{7 - \sqrt{89} }{2} = 3.5 - \sqrt{89}$

Answer 2

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

Step 1: Expand the left side of the equation.

$(x-2)^2 = (x-2)(x-2) = x^2 - 4x + 4$

Step 2: Distribute the 3 on the right side of the equation.

$3(x-2) = 3x - 6$

Now, the equation becomes:

$x^2 - 4x + 4 = 3x - 6$

Step 3: Move all terms to one side to set the equation to zero.

$x^2 - 4x + 4 - 3x + 6 = 0$

Step 4: Simplify the equation.

$x^2 - 7x + 10 = 0$

Step 5: Factor the quadratic equation.

$(x - 5)(x - 2) = 0$

Step 6: Use the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

So, $x - 5 = 0$ or $x - 2 = 0$

Step 7: Solve for x in each case.

For $x - 5 = 0$, adding 5 to both sides gives $x = 5$.

For $x - 2 = 0$, adding 2 to both sides gives $x = 2$.

Thus, the solutions to the equation are $x = 5$ and $x = 2$.