21,55 вроде так, крч а= 4;б=0,5, Перепроверь
х² + 4х - 180 = 0
Д = 4² - 4 * 1 * (-180) = 16 + 720 = 736
√Д = √736 = 4√46
х1 = (-4 + 4√36)/2 = -4(1 - √36) / 2 = -2(1 - √36) = -2 + 2√36
х2 = -2 - 2√36
1) 0,04a^2-2ay+25y^2
2)0,09x^2+2,4xy+16y^2
3) 1,69m^2+6,5mn+6,25n^2
4) 1 2/3? Или что? Непонятно
Делаешь так, пример:
(Х+у)^2=х(Х+у)+у(Х+у)=х^2+ху+ху+у^2= х^2+2ху+у^2
ОДЗ:
x<6, x>3, x≠4
![3log_{x-3}(6-x)+1\leq{1\over4}log^2_{x-3}(x^2-9x+18)^2\\3log_{x-3}(6-x)+1\leq log^2_{x-3}(6-x)(x-3)\\log_{x-3}(6-x)=t\\3t+1\leq(t+1)^2\\t^2-t\geq0\\t\in(-\infty;0]\cup[1;+\infty)\\\\log_{x-3}(6-x)\in(-\infty;0]\cup[1;+\infty)](https://tex.z-dn.net/?f=3log_%7Bx-3%7D%286-x%29%2B1%5Cleq%7B1%5Cover4%7Dlog%5E2_%7Bx-3%7D%28x%5E2-9x%2B18%29%5E2%5C%5C3log_%7Bx-3%7D%286-x%29%2B1%5Cleq+log%5E2_%7Bx-3%7D%286-x%29%28x-3%29%5C%5Clog_%7Bx-3%7D%286-x%29%3Dt%5C%5C3t%2B1%5Cleq%28t%2B1%29%5E2%5C%5Ct%5E2-t%5Cgeq0%5C%5Ct%5Cin%28-%5Cinfty%3B0%5D%5Ccup%5B1%3B%2B%5Cinfty%29%5C%5C%5C%5Clog_%7Bx-3%7D%286-x%29%5Cin%28-%5Cinfty%3B0%5D%5Ccup%5B1%3B%2B%5Cinfty%29)
Возможны 2 случая в зависимости от того, больше основание логарифма, чем 1 или меньше:
![1)x-3\ \textgreater \ 1\\\\6-x\leq1\\\cup\\6-x\geq x-3\\\\x\in(4;4.5]\cup[5;+\infty)\\\\2)x-3\ \textless \ 1\\\\6-x\geq1\\\cup\\6-x\leq x-3\\\\x\in(-\infty;4)]\\\\](https://tex.z-dn.net/?f=1%29x-3%5C+%5Ctextgreater+%5C+1%5C%5C%5C%5C6-x%5Cleq1%5C%5C%5Ccup%5C%5C6-x%5Cgeq+x-3%5C%5C%5C%5Cx%5Cin%284%3B4.5%5D%5Ccup%5B5%3B%2B%5Cinfty%29%5C%5C%5C%5C2%29x-3%5C+%5Ctextless+%5C+1%5C%5C%5C%5C6-x%5Cgeq1%5C%5C%5Ccup%5C%5C6-x%5Cleq+x-3%5C%5C%5C%5Cx%5Cin%28-%5Cinfty%3B4%29%5D%5C%5C%5C%5C)
Объединяем и пересекаем с ОДЗ:
![x\in(3;4)\cup(4;4.5]\cup[5;6)](https://tex.z-dn.net/?f=x%5Cin%283%3B4%29%5Ccup%284%3B4.5%5D%5Ccup%5B5%3B6%29)