1)![9x{^2}+12x=5](https://tex.z-dn.net/?f=9x%7B%5E2%7D%2B12x%3D5)
![9x{^2}+12x-5=0](https://tex.z-dn.net/?f=9x%7B%5E2%7D%2B12x-5%3D0)
![D=12{^2}-4*9*(-5)=144+180=324>0](https://tex.z-dn.net/?f=D%3D12%7B%5E2%7D-4%2A9%2A%28-5%29%3D144%2B180%3D324%3E0)
![x{_1}=\frac{-12+18}{18}=\frac{6}{18}=\frac{1}{3}](https://tex.z-dn.net/?f=x%7B_1%7D%3D%5Cfrac%7B-12%2B18%7D%7B18%7D%3D%5Cfrac%7B6%7D%7B18%7D%3D%5Cfrac%7B1%7D%7B3%7D)
![x{_2}=\frac{-12-18}{18}=-\frac{30}{18}=-\frac{5}{3}](https://tex.z-dn.net/?f=x%7B_2%7D%3D%5Cfrac%7B-12-18%7D%7B18%7D%3D-%5Cfrac%7B30%7D%7B18%7D%3D-%5Cfrac%7B5%7D%7B3%7D)
![|x{_1}-x{_2}|=|\frac{1}{3}-(-\frac{5}{3})|=|\frac{1}{3}+\frac{5}{3}|=|\frac{6}{3}|=|2|=2](https://tex.z-dn.net/?f=%7Cx%7B_1%7D-x%7B_2%7D%7C%3D%7C%5Cfrac%7B1%7D%7B3%7D-%28-%5Cfrac%7B5%7D%7B3%7D%29%7C%3D%7C%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B5%7D%7B3%7D%7C%3D%7C%5Cfrac%7B6%7D%7B3%7D%7C%3D%7C2%7C%3D2)
Ответ: 2.
2) 1) ![-24x{^2}+38x-15=0](https://tex.z-dn.net/?f=-24x%7B%5E2%7D%2B38x-15%3D0)
![24x{^2}-38x+15=0](https://tex.z-dn.net/?f=24x%7B%5E2%7D-38x%2B15%3D0)
![\frac{D}{4}=(-19){^2}-24*15=361-360=1>0](https://tex.z-dn.net/?f=%5Cfrac%7BD%7D%7B4%7D%3D%28-19%29%7B%5E2%7D-24%2A15%3D361-360%3D1%3E0)
![x{_1}=\frac{19+1}{24}=\frac{20}{24}=\frac{5}{6}](https://tex.z-dn.net/?f=x%7B_1%7D%3D%5Cfrac%7B19%2B1%7D%7B24%7D%3D%5Cfrac%7B20%7D%7B24%7D%3D%5Cfrac%7B5%7D%7B6%7D)
![x{_2}=\frac{19-1}{24}=\frac{18}{24}=\frac{3}{4}](https://tex.z-dn.net/?f=x%7B_2%7D%3D%5Cfrac%7B19-1%7D%7B24%7D%3D%5Cfrac%7B18%7D%7B24%7D%3D%5Cfrac%7B3%7D%7B4%7D)
2)
НОЗ=12
![\frac{10}{12}>\frac{9}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B12%7D%3E%5Cfrac%7B9%7D%7B12%7D)
Ответ: наименьший корень
.
2sin²x=√3cos(3π/2 +x)
2sin²x=√3sinx
2sin²x-√3sinx=0
sinx(2sinx-√3)=0
a) sinx=0
x=πk, k∈Z;
При k= -3 x= -3π ∈ [-3π; -1.5π];
При k= -2 x= -2π ∈ [-3π; -1.5π].
b) 2sinx-√3=0
2sinx=√3
sinx=(√3)/2
x=(-1)^k * (π/3) + πk, k∈Z;
При k=-3 x=(-1)⁻³ * (π/3)-3π= -π/3 - 3π ∉ [-3π; -1.5π] - не подходит
При k=-2 x=(-1)⁻² * (π/3)-2π=π/3 - 2π = -5π/3 ∈[-3π; -1.5π];
При k=-1 x=(-1)⁻¹ * (π/3)-π= -π/3 - π = -4π/3 ∉[-3π; -1.5π] - не подходит.
Ответ: -3π; -2π; -5π/3.
12y=15y+30-30
12y=15y
12y-15y=0
y=0
200-(((12+(12+9,8)+(31,8+9,8)+(41,6+9,8)+51,4)))=21,8