![\log_{5-x}\frac{x+2}{(x-5)^4}\ge-4](https://tex.z-dn.net/?f=%5Clog_%7B5-x%7D%5Cfrac%7Bx%2B2%7D%7B%28x-5%29%5E4%7D%5Cge-4)
Область определения неравенства:
![1)\ 5-x>0,\\x<5;\\\\2) \ 5-x\ne 1\\x\ne4;\\\\3)\ \frac{x+2}{(x-5)^4}>0,\\x+2>0,\\x>-2;\\\\4)\ (x-5)^4\ne0,\\x\ne5.](https://tex.z-dn.net/?f=1%29%5C%205-x%3E0%2C%5C%5Cx%3C5%3B%5C%5C%5C%5C2%29%20%5C%205-x%5Cne%201%5C%5Cx%5Cne4%3B%5C%5C%5C%5C3%29%5C%20%0A%5Cfrac%7Bx%2B2%7D%7B%28x-5%29%5E4%7D%3E0%2C%5C%5Cx%2B2%3E0%2C%5C%5Cx%3E-2%3B%5C%5C%5C%5C4%29%5C%20%0A%28x-5%29%5E4%5Cne0%2C%5C%5Cx%5Cne5.)
— не удовлетворяет
![(*)\to](https://tex.z-dn.net/?f=%28%2A%29%5Cto)
нет корней.
![2)\ 5-x>1,\ x<4\ (**),\\\frac{x+2}{(x-5)^4}\ge (5-x)^{-4},\\x\ge-1](https://tex.z-dn.net/?f=2%29%5C%205-x%3E1%2C%5C%20x%3C4%5C%20%28%2A%2A%29%2C%5C%5C%5Cfrac%7Bx%2B2%7D%7B%28x-5%29%5E4%7D%5Cge%20%285-x%29%5E%7B-4%7D%2C%5C%5Cx%5Cge-1)
C учётом
![(**):\ \left \{ {{x<4} \atop {x\ge-1}} \right. ,\ -1\le x<4.](https://tex.z-dn.net/?f=%28%2A%2A%29%3A%5C%20%20%5Cleft%20%5C%7B%20%7B%7Bx%3C4%7D%20%5Catop%20%7Bx%5Cge-1%7D%7D%20%5Cright.%20%2C%5C%20-1%5Cle%20x%3C4.)
Отбор корней согласно области определения:
![\left \{ {{x<5,\ x\ne4,\ x>-2,\ x\ne5} \atop {-1\le x<4}} \right. ,\ \ \ -1\le x<4.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx%3C5%2C%5C%20x%5Cne4%2C%5C%20x%3E-2%2C%5C%20x%5Cne5%7D%20%5Catop%20%7B-1%5Cle%20x%3C4%7D%7D%20%5Cright.%20%2C%5C%20%5C%20%5C%20%20-1%5Cle%20x%3C4.)
Ответ:
![x\in[-1;\ 4).](https://tex.z-dn.net/?f=x%5Cin%5B-1%3B%5C%204%29.)
A²-b²=(a+b)(a-b)
49-x²=7²-x²=(7+x)(7-x)
=======
(a=7,b=x)
(3-4cos2a+2cos²2a-1)/(3+4cos2a+2cos²2a-1)=
=(2cos²2a-4cos2a+2)/2cos²2a+4cos2a+2)=
=2(cos²2a-2cos2a+1)/2(cos²2a+2cos2a+1)=(cos2a-1)²/(cos2²+1)²=
=(-2sin²a)²/(2cos²a)²=4sin^4a/4cos^4a=tg^4a
Это умножить^?
тогда ответ такой
2)6x+2y>4a-2 5y-6x>3-4a
Выделяем целую часть у дроби слева.
Делим многочлена x4–5x3+3x–25 на x2–5x ''уголком''
x4–5x3+3x–25 | x2–5x
x4–5x3
––––––––
Неравенство примет вид:
x2+(3x–25)/(x2–5x) ≥ х2–(1/(x–4))+(5/x);
(3x–25)/x·(x–5)+(1/(x–4))–(5/x)≥ 0;
((3x–25)·(x–4)+(x2–5x)–5·(x–5)8(x–4))/(x·(x–4)·(x–5))≥ 0;
(–x2+3x)/(x·(x–4)·(x–5))≥ 0;
или
(х–3))/((x–4)·(x–5))≤ 0 при х≠0.
_–_0 _–_ [3] _+_ (4) _–__ (5) _+__
О т в е т. (–∞;0)U(0;3]U(4;5)