Ответ:
Объяснение:
!!!!!!!!!!!!!!!!!!!!!!!!!!!!
3/12=1/4=0,25
всего вариантов 24= 4!
нужно вариантов - 3(2,5,6) (2,6,10) (2,5,10)
![1). \\ \\x(x+8)(2-3x)>0 \\ \\x=0 \\x+8=0; x=-8 \\2-3x=0; -3x=-2; x=\frac{2}{3}](https://tex.z-dn.net/?f=1%29.+%5C%5C+%5C%5Cx%28x%2B8%29%282-3x%29%3E0+%5C%5C+%5C%5Cx%3D0+%5C%5Cx%2B8%3D0%3B+x%3D-8+%5C%5C2-3x%3D0%3B+-3x%3D-2%3B+x%3D%5Cfrac%7B2%7D%7B3%7D)
Расчёт знаков.
а). Пусть ![x=-9 \\ -9*(-9+8)(2-3*(-9))=-9*(-1)*29>0](https://tex.z-dn.net/?f=x%3D-9+%5C%5C+-9%2A%28-9%2B8%29%282-3%2A%28-9%29%29%3D-9%2A%28-1%29%2A29%3E0)
удовлетворяет
б). Пусть ![x=-1 \\ -1*(-1+8)(2-3*(-1)=-1*7*5<0](https://tex.z-dn.net/?f=x%3D-1+%5C%5C+-1%2A%28-1%2B8%29%282-3%2A%28-1%29%3D-1%2A7%2A5%3C0)
не удовлетворяет
в). Пусть ![x=\frac{1}{10} \\ \frac{1}{10}(\frac{1}{10}+8)(2-3*\frac{1}{10})=\frac{1}{10}*\frac{81}{10}\frac{17}{10}>0](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B10%7D+%5C%5C+%5Cfrac%7B1%7D%7B10%7D%28%5Cfrac%7B1%7D%7B10%7D%2B8%29%282-3%2A%5Cfrac%7B1%7D%7B10%7D%29%3D%5Cfrac%7B1%7D%7B10%7D%2A%5Cfrac%7B81%7D%7B10%7D%5Cfrac%7B17%7D%7B10%7D%3E0)
удовлетворяет
г). Пусть ![x=1 \\ 1(1+8)(2-3*1)=1*9*(-1)<0](https://tex.z-dn.net/?f=x%3D1+%5C%5C+1%281%2B8%29%282-3%2A1%29%3D1%2A9%2A%28-1%29%3C0)
не удовлетворяет
+ - + -
++++++++.------------.+++++++++.--------------
-8 0 2
Ответ: ![x < -8 ; 0 < x < \frac{2}{3}](https://tex.z-dn.net/?f=x+%3C+-8+%3B+0+%3C+x+%3C+%5Cfrac%7B2%7D%7B3%7D)
![2). \\ (x^2+4x)(x^2+4x-17)+60=0](https://tex.z-dn.net/?f=2%29.+%5C%5C+%28x%5E2%2B4x%29%28x%5E2%2B4x-17%29%2B60%3D0)
заменим переменную: ![a=(x^2+4x)](https://tex.z-dn.net/?f=a%3D%28x%5E2%2B4x%29)
получим уравнение:
![a(a-17)+60=0 \\a^2-17a+60=0 \\ \\D=(-17)^2-4*1+60=289-240=49 \\x_1=\frac{17-7}{2}=5 \\ \\x_2=\frac{17+7}{2}=12](https://tex.z-dn.net/?f=a%28a-17%29%2B60%3D0+%5C%5Ca%5E2-17a%2B60%3D0+%5C%5C+%5C%5CD%3D%28-17%29%5E2-4%2A1%2B60%3D289-240%3D49+%5C%5Cx_1%3D%5Cfrac%7B17-7%7D%7B2%7D%3D5+%5C%5C+%5C%5Cx_2%3D%5Cfrac%7B17%2B7%7D%7B2%7D%3D12)
подставляем
и решаем ещё два уравнения:
а).
![x^2+4x=5 \\x^2+4x-5=0 \\ \\D=4^2-4*1*(-5)=16+20=36 \\x_1=\frac{-4-6}{2}=-5 \\ \\x_2=\frac{-4+6}{2}=1](https://tex.z-dn.net/?f=x%5E2%2B4x%3D5+%5C%5Cx%5E2%2B4x-5%3D0+%5C%5C+%5C%5CD%3D4%5E2-4%2A1%2A%28-5%29%3D16%2B20%3D36+%5C%5Cx_1%3D%5Cfrac%7B-4-6%7D%7B2%7D%3D-5+%5C%5C+%5C%5Cx_2%3D%5Cfrac%7B-4%2B6%7D%7B2%7D%3D1)
б).
![x^2+4x=12 \\x^2+4x-12=0 \\ \\D=-4^2-4*1*(-12)=16+48=64 \\x_1=\frac{-4-8}{2}=-6 \\ \\x_2=\frac{-4+8}{2}=2](https://tex.z-dn.net/?f=x%5E2%2B4x%3D12+%5C%5Cx%5E2%2B4x-12%3D0+%5C%5C+%5C%5CD%3D-4%5E2-4%2A1%2A%28-12%29%3D16%2B48%3D64+%5C%5Cx_1%3D%5Cfrac%7B-4-8%7D%7B2%7D%3D-6+%5C%5C+%5C%5Cx_2%3D%5Cfrac%7B-4%2B8%7D%7B2%7D%3D2)
Ответ: ![x=-5 ; x=-6 ; x=1 ; x=2](https://tex.z-dn.net/?f=x%3D-5+%3B+x%3D-6+%3B+x%3D1+%3B+x%3D2)
1-1,7x-0.8x-2=3.4
-2.5x=4.4
x=-1.76
X-0.5=0.6x-0.4
x-0.6x=-0.4+0.5
0.4x=0.1
x=0.25