0 }} \right." alt="\left \{ {{6+x-x^{2} \geq0 } \atop {x^{3}-3x^{2}-4x>0 }} \right." align="absmiddle" class="latex-formula">
6+x-x²≥0 | : (-1)
x²-x-6≤0
x²-x-6=0
D = (-1)² - 4 * (-6) = 1 + 24 = 25 = 5²
![x_{1} = \frac{1+5}{2} = 3 x_{1} = \frac{1+5}{2} = 3](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20%5Cfrac%7B1%2B5%7D%7B2%7D%20%3D%203)
![x_{1} = \frac{1-5}{2} = -2 x_{1} = \frac{1-5}{2} = -2](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20%5Cfrac%7B1-5%7D%7B2%7D%20%3D%20-2)
x∈[-2;3]
x³-3x²-4x>0
x*(x²-3x-4)=0
x=0
x²-3x-4=0
D = (-3)² - 4*(-4) = 9 + 16 = 25 = 5²
![x_{1} = \frac{3+5}{2} = 4 x_{1} = \frac{3+5}{2} = 4](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20%5Cfrac%7B3%2B5%7D%7B2%7D%20%3D%204)
![x_{1} = \frac{3-5}{2} = -1 x_{1} = \frac{3-5}{2} = -1](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20%5Cfrac%7B3-5%7D%7B2%7D%20%3D%20-1)
x∈(-1;0) ∪ (4; +∞)
![\left \{ {{-2\leq x\leq3 } \atop {\left[\begin{array}{ccc}-1 \left \{ {{-2\leq x\leq3 } \atop {\left[\begin{array}{ccc}-1](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B-2%5Cleq%20x%5Cleq3%20%7D%20%5Catop%20%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%3Cx%3C0%5C%5Cx%3E4%5C%5C%5Cend%7Barray%7D%7D%7D%20%5Cright.)
Находим пересечение. Это отрезок от -1 до 0
Ответ: x∈(-1;0)