2sin^2x-5sinx*cosx-8cox^x=-1(sin^2x+cos^2x)
2sin^2x-5sinx*cosx-8cox^x+1(sin^2x+cos^2x)=0
3sin^2x-5sinx*cosx-7cos^2x=0
3tan^2x-5tanx-7=0
3t^2-5t-7=0
t=(5+√109)/6
t=(5-√109)/6
x=arctan(5+√109/6)+kπ, k∈Z
x=arctan(5-√109/6)+kπ, k∈Z
А) 3а²+30ab+75b² = 3(a²+10ab+25b²) = 3(a+5)²
б) 27-с³ = (3-с)(9+3с+с²)
в) ху-5у-х+5 = у(х-5)-(х-5) = (х-5)(у-1)
Y=-x²+6x-5 y=0 x=2 x=3
S=int I₂³(-x²+6x-5-0)=-x³/3+3x²-5x I₂³=-3³/3+3*3²-5+2³/3-3*2²+5*2=
=9+27-5+8/3-12+10=31и2/3.
Из первого выводим x:
x=6-y
Подставляем во второе вместо x:
![{(6 - y)}^{2} + 2y = 60 \\ 36 - 12y + {y}^{2} + 2y - 60 = 0 \\ {y}^{2} - 10y - 24 = 0](https://tex.z-dn.net/?f=+%7B%286+-+y%29%7D%5E%7B2%7D++%2B+2y+%3D+60+%5C%5C+36+-+12y+%2B++%7By%7D%5E%7B2%7D++%2B+2y+-+60+%3D+0+%5C%5C++%7By%7D%5E%7B2%7D++-+10y+-+24+%3D+0)
D:
![{10}^{2} - 4 \times ( - 24) = 100 + 96 = \\ = 196](https://tex.z-dn.net/?f=+%7B10%7D%5E%7B2%7D++-+4+%5Ctimes+%28+-+24%29+%3D+100+%2B+96+%3D+%5C%5C++%3D++196)
x1:
![\frac{10 + 14}{2} = 12](https://tex.z-dn.net/?f=+%5Cfrac%7B10+%2B+14%7D%7B2%7D++%3D+12)
x2
![\frac{10 - 14}{2} = - 2](https://tex.z-dn.net/?f=+%5Cfrac%7B10+-+14%7D%7B2%7D++%3D++-+2)
X=1
поднеси обе стороні уравнения к квадрату