Question

(x-1)^2=1 пешить уравнение

Answer 1

X-1=+-1
x-1=-1
x=0
x-1=1
x=1+1=2
Ответ: 0; 2

Answer 2

$(x-1)^2=1; \\ x^{2} - 2x + 1 = 1; \\ x^{2} - 2x + 1 - 1 = 0; \\ x^{2}-2x=0; \\ x(x-2)=0.$

Теперь находим корни. Приравниваем x и значение в скобках до нуля.

x(x-2) = 0
x = 0 или x - 2 = 0
                x = 2

Ответ : 0 и 2

Answer 3

To solve the equation $(x - 1)^2 = 1$, we'll first expand the left side and then proceed to solve for $x$. Here's the step-by-step solution:

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

Step 2: Set the expanded equation equal to 1 $x^2 - 2x + 1 = 1$

Step 3: Simplify the equation Subtract 1 from both sides to isolate the quadratic term: $x^2 - 2x = 0$

Step 4: Factor out $x$ from the left side $x(x - 2) = 0$

Step 5: Apply the zero-product property Set each factor equal to zero and solve for $x$:

$x = 0$ or $x - 2 = 0$

Step 6: Solve for $x$ in the second equation $x - 2 = 0 \implies x = 2$

So the solutions to the equation are $x = 0$ and $x = 2$.