Question

(×+6)(×-1)(×+3,6)>0​

Answer 1

Ответ:

Не могла написать таких знаков нет , смотри полную картинку

Answer 2

To determine the intervals where the expression $(x+6)(x-1)(x+3.6) > 0$ is true, we need to find the intervals where the expression is positive (greater than zero).

Step 1: Find the critical points where the expression equals zero. Set each factor in the expression to zero and solve for $x$:

1. $x + 6 = 0$, $x = -6$
2. $x - 1 = 0$, $x = 1$
3. $x + 3.6 = 0$, $x = -3.6$

Step 2: Determine the intervals on the number line using these critical points. The expression can change its sign at these critical points. We will use these critical points to create intervals:

1. Interval $(-∞, -6)$
2. Interval $(-6, 1)$
3. Interval $(1, -3.6)$
4. Interval $(-3.6, ∞)$

Step 3: Test the expression in each interval to determine its sign.

1. In the interval $(-∞, -6)$: Choose $x = -7$ (any value less than -6) $(x+6)(x-1)(x+3.6) = (-7 + 6)(-7 - 1)(-7 + 3.6) = (-1)(-8)(-3.4) = -27.2$, which is less than zero.

2. In the interval $(-6, 1)$: Choose $x = 0$ (any value between -6 and 1) $(x+6)(x-1)(x+3.6) = (0 + 6)(0 - 1)(0 + 3.6) = (6)(-1)(3.6) = -21.6$, which is less than zero.

3. In the interval $(1, -3.6)$: Choose $x = 2$ (any value between 1 and -3.6) $(x+6)(x-1)(x+3.6) = (2 + 6)(2 - 1)(2 + 3.6) = (8)(1)(5.6) = 44.8$, which is greater than zero.

4. In the interval $(-3.6, ∞)$: Choose $x = 0$ (any value greater than -3.6) $(x+6)(x-1)(x+3.6) = (0 + 6)(0 - 1)(0 + 3.6) = (6)(-1)(3.6) = -21.6$, which is less than zero.

Step 4: Analyze the result. The expression $(x+6)(x-1)(x+3.6)$ is greater than zero in the interval $(1, -3.6)$. Therefore, the solution to the inequality $(x+6)(x-1)(x+3.6) > 0$ is $x \in (1, -3.6)$.