Question

Решите уравнение x^2-2x+2=0

Answer 1

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Answer 2

To solve the quadratic equation $x^2 - 2x + 2 = 0$, we can use the quadratic formula. The quadratic formula is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a},$

where $a$, $b$, and $c$ are the coefficients of the quadratic equation $ax^2 + bx + c = 0$.

For our equation $x^2 - 2x + 2 = 0$, the coefficients are $a = 1$, $b = -2$, and $c = 2$.

Now, let's plug these values into the quadratic formula:

$x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4 \cdot 1 \cdot 2}}{2 \cdot 1}$

$x = \frac{2 \pm \sqrt{4 - 8}}{2}$

$x = \frac{2 \pm \sqrt{-4}}{2}$

Since the square root of a negative number is not a real number, this equation does not have any real solutions. Instead, it has two complex solutions:

$x = \frac{2 + \sqrt{-4}}{2} = \frac{2 + 2i}{2} = 1 + i,$

and

$x = \frac{2 - \sqrt{-4}}{2} = \frac{2 - 2i}{2} = 1 - i.$

So the solutions to the equation are $x = 1 + i$ and $x = 1 - i$, where $i$ is the imaginary unit ($i^2 = -1$).