Question

Решите уравнение х^2-6x+7

Answer 1

х^2-6х+7=0

D= 36- 4×7= 8

x1= (6+√8)/2 = 3+√2

х2= (6-√8)/2= 3-√2

Ответ: х1= 3+√2 ; х2= 3-√2

Answer 2

To solve the quadratic equation $x^2 - 6x + 7 = 0$, 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 equation, $a = 1$, $b = -6$, and $c = 7$. Substituting these values into the quadratic formula, we get:

$x = \frac{-(-6) \pm \sqrt{(-6)^2 - 4 \cdot 1 \cdot 7}}{2 \cdot 1}$ $x = \frac{6 \pm \sqrt{36 - 28}}{2}$ $x = \frac{6 \pm \sqrt{8}}{2}$ $x = \frac{6 \pm 2\sqrt{2}}{2}$

Now, we have two solutions for $x$:

1. $x = \frac{6 + 2\sqrt{2}}{2} = 3 + \sqrt{2}$
2. $x = \frac{6 - 2\sqrt{2}}{2} = 3 - \sqrt{2}$

So, the solutions to the equation $x^2 - 6x + 7 = 0$ are $x = 3 + \sqrt{2}$ and $x = 3 - \sqrt{2}$.