Question

(x-2)(x+3) >(x-1) (2+x)​

Answer 1

Ответ:

незнаю

Объяснение:

приветшшушкгкг4ш44

Answer 2

Ответ:

Смотри решение на фото

Answer 3

To solve the inequality $(x - 2)(x + 3) > (x - 1)(2 + x)$, you can follow these steps:

1. Expand both sides of the inequality:

   $(x - 2)(x + 3) > (x - 1)(2 + x)$

   $x^2 + 3x - 2x - 6 > 2x - x^2 - x + 2$

2. Simplify the expressions on both sides:

   $x^2 + x - 6 > x - x^2 + 2$

3. Move all the terms to one side of the inequality to set it to zero:

   $x^2 + x - 6 - x + x^2 - 2 > 0$

4. Combine like terms:

   $2x^2 - 7 > 0$

5. Now, we need to find the values of $x$ that make this inequality true. To do this, you can use the quadratic formula to find the roots of the quadratic equation $2x^2 - 7 = 0$:

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

   In this case, $a = 2$, $b = 0$, and $c = -7$. Plugging these values into the formula:

   $x = \frac{-0 \pm \sqrt{0^2 - 4(2)(-7)}}{2(2)}$

   $x = \frac{\pm \sqrt{56}}{4}$

   $x = \pm \frac{\sqrt{14}}{2}$

6. Now that we have the roots, we can determine the intervals where the inequality $2x^2 - 7 > 0$ is satisfied. We can do this by testing values in each interval:

   a) Choose a value less than $-\frac{\sqrt{14}}{2}$, for example, $x = -1$.

   $2(-1)^2 - 7 = 2 - 7 = -5$

   Since $-5$ is less than $0$, the inequality is not satisfied in this interval.

   b) Choose a value between $-\frac{\sqrt{14}}{2}$ and $\frac{\sqrt{14}}{2}$, for example, $x = 0$.

   $2(0)^2 - 7 = -7$

   Since $-7$ is less than $0$, the inequality is satisfied in this interval.

   c) Choose a value greater than $\frac{\sqrt{14}}{2}$, for example, $x = 1$.

   $2(1)^2 - 7 = 2 - 7 = -5$

   Since $-5$ is less than $0$, the inequality is not satisfied in this interval.

So, the solution to the inequality $(x - 2)(x + 3) > (x - 1)(2 + x)$ is $x \in (-\frac{\sqrt{14}}{2}, \frac{\sqrt{14}}{2})$