............................................................
![log^2_{0.5} x-log_{0.5} x-2 \geq 0](https://tex.z-dn.net/?f=log%5E2_%7B0.5%7D+x-log_%7B0.5%7D+x-2+%5Cgeq+0)
ОДЗ:
![x\ \textgreater \ 0](https://tex.z-dn.net/?f=x%5C+%5Ctextgreater+%5C+0)
![x](https://tex.z-dn.net/?f=x)
∈
![(0;+](https://tex.z-dn.net/?f=%280%3B%2B)
∞
![)](https://tex.z-dn.net/?f=%29)
Замена:
![log_{0.5} x=t](https://tex.z-dn.net/?f=log_%7B0.5%7D+x%3Dt)
![t^2-t-2 \geq 0](https://tex.z-dn.net/?f=t%5E2-t-2+%5Cgeq+0)
![D=(-1)^2-4*1*(-2)=1+8=9](https://tex.z-dn.net/?f=D%3D%28-1%29%5E2-4%2A1%2A%28-2%29%3D1%2B8%3D9)
![t_1= \frac{1+3}{2}=2](https://tex.z-dn.net/?f=t_1%3D+%5Cfrac%7B1%2B3%7D%7B2%7D%3D2+)
+ - +
-----------[-1]-------------[2]-------------
///////////// ///////////////
![t \leq -1](https://tex.z-dn.net/?f=t+%5Cleq+-1)
или
![t \geq 2](https://tex.z-dn.net/?f=t+%5Cgeq+2)
![log_{0.5}x \leq -1](https://tex.z-dn.net/?f=log_%7B0.5%7Dx+%5Cleq+-1+)
или
![log_{0.5}x \geq 2](https://tex.z-dn.net/?f=log_%7B0.5%7Dx++%5Cgeq+2)
![log_{0.5}x \leq log_{0.5}2](https://tex.z-dn.net/?f=log_%7B0.5%7Dx++%5Cleq+log_%7B0.5%7D2)
или
![log_{0.5}x \geq log_{0.5}0.25](https://tex.z-dn.net/?f=log_%7B0.5%7Dx++%5Cgeq+log_%7B0.5%7D0.25)
![x \geq 2](https://tex.z-dn.net/?f=x+%5Cgeq+2)
или
![x \leq 0.25](https://tex.z-dn.net/?f=x+%5Cleq+0.25)
------------[0.25]-----------------[2]-----------------
/////////////// /////////////////////
С учётом ОДЗ получаем
Ответ:
![(0;0.25]](https://tex.z-dn.net/?f=%280%3B0.25%5D)
∪
![[2;+](https://tex.z-dn.net/?f=%5B2%3B%2B)
∞
![)](https://tex.z-dn.net/?f=%29)
Y=x-2,5
x 0 3
y -2,5 0,5
Точки пересечения с осями (0;-2,5),(2,5;0)
А что хоть найти? Сократить? Если да, то у меня так...