90:2=45;90:3=30;90:5=18;90:9=10;90:10=9
X³+3x²-9x-27=0
x²(x+3)-9(x+3)=0
(x+3)(x²-9)=0
x+3=0
x=-3
x²-9=0
x=3
x=-3
Ответ:х=3 и х=-3.
![\frac{|x+3|+x}{x+2} - 1>0](https://tex.z-dn.net/?f=+%5Cfrac%7B%7Cx%2B3%7C%2Bx%7D%7Bx%2B2%7D+-+1%3E0+)
![\frac{|x+3|+x}{x+2} - \frac{x+2}{x+2}>0](https://tex.z-dn.net/?f=%5Cfrac%7B%7Cx%2B3%7C%2Bx%7D%7Bx%2B2%7D+-+%5Cfrac%7Bx%2B2%7D%7Bx%2B2%7D%3E0+)
![\frac{|x+3|+x-x-2}{x+2} >0](https://tex.z-dn.net/?f=++%5Cfrac%7B%7Cx%2B3%7C%2Bx-x-2%7D%7Bx%2B2%7D+%3E0+)
![\frac{|x+3|-2}{x+2} >0](https://tex.z-dn.net/?f=%5Cfrac%7B%7Cx%2B3%7C-2%7D%7Bx%2B2%7D+%3E0+)
|x+3|-2>0 или |x+3|-2<0
x+2>0 x+2<0
|x+3| > 2 или |x+3| < 2
x>-2 x<-2
x+3 > 2 или x+3 < -2 или -2< x+3 < 2
x>-2 x>-2 x<-2
x > -1 или x< -5 или -5< x < -1
x > -2 x>-2 x<-2
<u>x > -1 </u> или Ф или <u> -5< x < -2</u>
Ответ: ( -5 ; -2) ∨ (-1 ; + оо)
ОДЗ
x>0
x-8>0
x>8
![log_3(x-8)+log_3x=2 \\ \\ log_3x(x-8)=2 \\ \\ log_3( x^{2} -8x)=log_3 3^2 \\ \\ x^{2} -8x=9 \\ \\ x^{2} -8x-9=0 \\ \\ D=8^2+4*9=100 \\ \\ x_1= \frac{8+10}{2}=9 \\ \\ x_2= \frac{8-10}{2} =-1](https://tex.z-dn.net/?f=log_3%28x-8%29%2Blog_3x%3D2+%5C%5C++%5C%5C+log_3x%28x-8%29%3D2+%5C%5C++%5C%5C+log_3%28+x%5E%7B2%7D+-8x%29%3Dlog_3+3%5E2+%5C%5C++%5C%5C++x%5E%7B2%7D+-8x%3D9+%5C%5C++%5C%5C++x%5E%7B2%7D+-8x-9%3D0+%5C%5C++%5C%5C+D%3D8%5E2%2B4%2A9%3D100+%5C%5C++%5C%5C+x_1%3D+%5Cfrac%7B8%2B10%7D%7B2%7D%3D9+%5C%5C++%5C%5C+x_2%3D+%5Cfrac%7B8-10%7D%7B2%7D+%3D-1)
В соответствии с ОДЗ х₂<8, значит не подходит
Ответ х=9
(8+6-10-2)/(4х-2)=2/2(2х-1)=1/(2х-1)