Question

(x+1)(x-2)²>0, помогите пожалуйста

Answer 1

(x+1)(x-2)²>0

Метод интервалов

------------------(-1) ++++++++++ ×2× +++++++++

x ∈ (-1, 2) U (2, +∞)

Answer 2

To determine the solution to the inequality (x+1)(x-2)² > 0, we can use the concept of interval notation and the signs of the factors.

Let's break it down step by step:

Factoring the expression:

First, let's factor the expression (x+1)(x-2)².

The expression can be factored as follows: (x+1)(x-2)² = (x+1)(x-2)(x-2).

Analyzing the factors:

Now, let's analyze the factors (x+1), (x-2), and (x-2).

- The factor (x+1) represents the interval where x is greater than -1. - The factor (x-2) represents the interval where x is greater than 2. - The factor (x-2) represents the interval where x is greater than 2.

Determining the intervals:

To determine the intervals where the inequality is true, we need to consider the signs of the factors.

- When (x+1) is positive, the inequality is true. - When (x-2) is positive, the inequality is true. - When (x-2) is positive, the inequality is true.

Combining the intervals:

To find the intervals where the inequality (x+1)(x-2)² > 0 is true, we need to combine the intervals where the factors are positive.

From the analysis above, we can see that the inequality is true when x > 2 or x < -1.

Final Answer:

Therefore, the solution to the inequality (x+1)(x-2)² > 0 is x < -1 or x > 2.

Please note that this is a general explanation. If you have a specific value of x that you would like to evaluate, please let me know and I can provide a more specific answer.