Question

1\(x-2)(x-3)>0 решите неравенство

Answer 1

Ответ:

Пошаговое объяснение: решение и ответ на фото

Answer 2

To solve the inequality $(x-2)(x-3) > 0$, we can use the method of intervals.

Step 1: Find the critical points by setting the expression inside the inequality to zero and solving for $x$: $(x-2)(x-3) = 0$

To do this, we set each factor equal to zero: $x - 2 = 0 \Rightarrow x = 2$ $x - 3 = 0 \Rightarrow x = 3$

Step 2: Create intervals using these critical points and test points within each interval:

We now have three intervals: $(-\infty, 2)$, $(2, 3)$, and $(3, \infty)$. To determine whether the expression is greater than zero within each interval, we can test a point in each interval:

• For the interval $(-\infty, 2)$, we can pick $x = 0$.
• For the interval $(2, 3)$, we can pick $x = 2.5$.
• For the interval $(3, \infty)$, we can pick $x = 4$.

Step 3: Determine the sign of the expression in each interval:

1. For $x = 0$: $(0 - 2)(0 - 3) = (-2)(-3) = 6 > 0$

2. For $x = 2.5$: $(2.5 - 2)(2.5 - 3) = (0.5)(-0.5) = -0.25 < 0$

3. For $x = 4$: $(4 - 2)(4 - 3) = (2)(1) = 2 > 0$

Step 4: Determine the solution based on the signs:

Since the original inequality is $(x-2)(x-3) > 0$, we are looking for intervals where the expression is greater than zero (positive).

The solution to the inequality is $x \in (-\infty, 2) \cup (3, \infty)$.

So, the inequality $(x-2)(x-3) > 0$ is true when $x$ belongs to the open intervals $(- \infty, 2)$ or $(3, \infty)$.