Question

Решите уравнение x^2-7x+16=0

Answer 1

Найдем дискриминант квадратного уравнения:

D = b^2 - 4ac = (-7)2 - 4·1·16 = 49 - 64 = -15

Так как дискриминант меньше нуля, то уравнение не имеет действительных решений.

Answer 2

To solve the quadratic equation $x^2 - 7x + 16 = 0$, we can use the quadratic formula:

The quadratic formula states that for an equation in the form $ax^2 + bx + c = 0$, the solutions for $x$ can be found using:

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

In our equation, $a = 1$, $b = -7$, and $c = 16$.

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

$x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4 \cdot 1 \cdot 16}}{2 \cdot 1}$

Simplifying further:

$x = \frac{7 \pm \sqrt{49 - 64}}{2}$ $x = \frac{7 \pm \sqrt{-15}}{2}$

Since we have a negative value inside the square root ($-15$), this equation has no real solutions. The solutions involve complex numbers instead. So, the solutions for $x$ are:

$x = \frac{7 + i\sqrt{15}}{2}$ and $x = \frac{7 - i\sqrt{15}}{2}$

where $i$ is the imaginary unit, defined as $i^2 = -1$.