Question

Решить уравнение: x^2-4x+8=0

Answer 1

Х^2-4х+8=0;
D= (-4)^2-4*1*8=16-32=-16<0
Это уравнение не имеет корней

Answer 2

To solve the quadratic equation $x^2 - 4x + 8 = 0$, we can use the quadratic formula:

The quadratic formula states that for an equation of the form $ax^2 + bx + c = 0$, the solutions for $x$ are given by:

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

In our case, $a = 1$, $b = -4$, and $c = 8$. Substituting these values into the quadratic formula, we get:

$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \cdot 1 \cdot 8}}{2 \cdot 1}$ $x = \frac{4 \pm \sqrt{16 - 32}}{2}$ $x = \frac{4 \pm \sqrt{-16}}{2}$

Since the discriminant ($b^2 - 4ac$) is negative ($-16$), the equation has no real solutions. Instead, it has two complex solutions, which involve the imaginary unit $i$:

$x = \frac{4 + \sqrt{-16}}{2} = \frac{4 + 4i}{2} = 2 + 2i$

$x = \frac{4 - \sqrt{-16}}{2} = \frac{4 - 4i}{2} = 2 - 2i$

So, the solutions to the equation are $x = 2 + 2i$ and $x = 2 - 2i$.