Question

Решение неравенства X квадрат минус икс меньше 42

Answer 1

Вроде бы всё правильно решил

Answer 2

X² -x < 42
x² - x - 42 < 0
x² - x - 42 = 0
D = 1 + 4*42 = 13²
x1 = 7
x2 = -6
Ответ  x∈(-6;7)

Answer 3

I can help you with solving inequalities. Here is a detailed solution for your inequality:

The inequality is $x^2-x<42$. To solve it, we need to find the roots of the corresponding equation $x^2-x=42$. We can use the quadratic formula to find them:

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

where $a=1$, $b=-1$, and $c=-42$. Plugging these values into the formula, we get:

$$x=\frac{1\pm\sqrt{1+168}}{2}=\frac{1\pm 13}{2}$$

So the roots are $x_1=7$ and $x_2=-6$. These are the points where the parabola $y=x^2-x$ intersects the horizontal line $y=42$. To find the solution of the inequality, we need to check the sign of $y$ in each of the three intervals: $(-\infty,-6)$, $(-6,7)$, and $(7,\infty)$.

We can use any point in each interval to test the sign of $y$. For example, we can use $x=-7$, $x=0$, and $x=8$. Plugging these values into the equation $y=x^2-x$, we get:

$$y(-7)=49+7=56>42$$ $$y(0)=0-0=0<42$$ $$y(8)=64-8=56>42$$

So we see that $y$ is negative (less than 42) only in the interval $(-6,7)$. Therefore, the solution of the inequality is:

$$-6

or in interval notation:

$$x\in(-6,7)$$

You can also see the graph of the inequality here. You can also use an online calculator to solve inequalities here.

I hope this helps you understand how to solve quadratic inequalities. If you have any other questions, feel free to ask me.