Question

(x-3)(x+1)²⩾0Решите неравенство, пожалуйста!!​

Answer 1

Произведение неотрицательно  тогда и только тогда когда множители имеют одинаковые знаки:

$\left \{ {{x-3\geq 0} \atop {(x+1)^2\geq 0} \right.$    или  $\left \{ {{x-3\leq 0} \atop {(x+1)^2\leq 0} \right.$

(x+1)²>0  при всех х≠-1

при х=-1  (-1-3)·0≥0  -  верно

$\left \{ {{x\geq 3} \atop {x\in (-\infty;+\infty)}} \right.$   или  $\left \{ {{x\leq 3} \atop {x=-1}} \right.$

$x\geq 3$           или   $x=-1$

 

О т в е т. {-1}U[3;+∞)

Answer 2

Ответ:

Объяснение:

(x-3)(x+1)²⩾0

решим методом интервалов

нули : x-3=0; x=3

          x+1=0; x=-1

------[-1]----[3]++++>x

Ответ: x ∈ {-1}∪[3; +∞)

Answer 3

To solve the inequality (x-3)(x+1)² ≥ 0, we can use the concept of sign charts or interval notation. Let's break it down step by step.

Step 1: Find the critical points

To determine where the expression (x-3)(x+1)² equals zero, we set each factor equal to zero and solve for x:

x - 3 = 0 => x = 3 x + 1 = 0 => x = -1

So, the critical points are x = 3 and x = -1.

Step 2: Create a sign chart

We will create a sign chart to determine the sign of the expression (x-3)(x+1)² in different intervals.

| Interval | (x-3) | (x+1)² | (x-3)(x+1)² | |----------|-------|--------|--------------| | x < -1 | - | + | - | | -1 < x < 3 | - | + | - | | x > 3 | + | + | + |

In the sign chart, "+" represents a positive sign, and "-" represents a negative sign.

Step 3: Analyze the sign chart

From the sign chart, we can see that the expression (x-3)(x+1)² is negative in the intervals x < -1 and -1 < x < 3, and positive when x > 3.

Step 4: Determine the solution

To solve the inequality (x-3)(x+1)² ≥ 0, we need to find the values of x that make the expression non-negative (greater than or equal to zero).

From the sign chart, we can see that the expression is non-negative (≥ 0) when x ≤ -1 or x ≥ 3.

Therefore, the solution to the inequality (x-3)(x+1)² ≥ 0 is x ≤ -1 or x ≥ 3.

I hope this helps! Let me know if you have any further questions.