Ответ:-1
Объяснение:
Тут должно быть объяснение
<span>3x-y=15 у=3х-15 у=3х-15 у=3х-15 у=3х-15 у=-6</span>
<span>6x+y=12 6х+у=12 6х+3х-15=12 9х=27 х=3 х=3</span>
Ответ ответ ответ ответ ответ ответ
Делаем замену:
a=2x
получим:
![5sina-sin3a+6=0 \\5sina-(3sina-4sin^3a)+6=0 \\5sina-3sina+4sin^3a+6=0 \\4sin^3a+2sina+6=0](https://tex.z-dn.net/?f=5sina-sin3a%2B6%3D0%0A%5C%5C5sina-%283sina-4sin%5E3a%29%2B6%3D0%0A%5C%5C5sina-3sina%2B4sin%5E3a%2B6%3D0%0A%5C%5C4sin%5E3a%2B2sina%2B6%3D0)
еще одна замена:
![sina=y,\ y \in [-1;1]](https://tex.z-dn.net/?f=sina%3Dy%2C%5C+y+%5Cin+%5B-1%3B1%5D)
тогда:
![4y^3+2y+6=0 \\P(1)=4+2+6\neq 0 \\P(-1)=-4-2+6=0 \Rightarrow y_1=-1 \\(y+1)(4y^2+py+q)=4y^3+py^2+qy+4y^2+py+q=\\=4y^3+y^2(p+4)+y(q+p)+q \\4y^3+2y+6=4y^3+y^2(p+4)+y(q+p)+q \\ \left \{ {{p+4=0} \atop {q+p=2}} \right. \Rightarrow \left \{ {{p=-3} \atop {q=6}} \right. \\(y+1)(4y^2-3y+6)=0 \\4y^2-3y+6=0 \\D\ \textless \ 0](https://tex.z-dn.net/?f=4y%5E3%2B2y%2B6%3D0%0A%5C%5CP%281%29%3D4%2B2%2B6%5Cneq+0%0A%5C%5CP%28-1%29%3D-4-2%2B6%3D0+%5CRightarrow+y_1%3D-1%0A%5C%5C%28y%2B1%29%284y%5E2%2Bpy%2Bq%29%3D4y%5E3%2Bpy%5E2%2Bqy%2B4y%5E2%2Bpy%2Bq%3D%5C%5C%3D4y%5E3%2By%5E2%28p%2B4%29%2By%28q%2Bp%29%2Bq%0A%5C%5C4y%5E3%2B2y%2B6%3D4y%5E3%2By%5E2%28p%2B4%29%2By%28q%2Bp%29%2Bq%0A%5C%5C+%5Cleft+%5C%7B+%7B%7Bp%2B4%3D0%7D+%5Catop+%7Bq%2Bp%3D2%7D%7D+%5Cright.+%5CRightarrow++%5Cleft+%5C%7B+%7B%7Bp%3D-3%7D+%5Catop+%7Bq%3D6%7D%7D+%5Cright.+%0A%5C%5C%28y%2B1%29%284y%5E2-3y%2B6%29%3D0%0A%5C%5C4y%5E2-3y%2B6%3D0%0A%5C%5CD%5C+%5Ctextless+%5C+0)
обратная замена:
![sina=-1 \\sin2x=-1 \\2x=- \frac{\pi}{2} +2\pi ,\ n \in Z \\x=- \frac{\pi}{4} +\pi n,\ n \in Z](https://tex.z-dn.net/?f=sina%3D-1%0A%5C%5Csin2x%3D-1%0A%5C%5C2x%3D-+%5Cfrac%7B%5Cpi%7D%7B2%7D+%2B2%5Cpi+%2C%5C+n+%5Cin+Z%0A%5C%5Cx%3D-+%5Cfrac%7B%5Cpi%7D%7B4%7D+%2B%5Cpi+n%2C%5C+n+%5Cin+Z)
ищем наименьший положительный корень:
![n=0; x=- \frac{\pi}{4}\ \textless \ 0 \\n=-1; x=- \frac{\pi}{4}-\pi\ \textless \ 0 \\n=1; x=- \frac{\pi}{4}+\pi= \frac{3\pi}{4}](https://tex.z-dn.net/?f=n%3D0%3B+x%3D-+%5Cfrac%7B%5Cpi%7D%7B4%7D%5C+%5Ctextless+%5C+0%0A%5C%5Cn%3D-1%3B+x%3D-+%5Cfrac%7B%5Cpi%7D%7B4%7D-%5Cpi%5C+%5Ctextless+%5C+0%0A%5C%5Cn%3D1%3B+x%3D-+%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cpi%3D+%5Cfrac%7B3%5Cpi%7D%7B4%7D+)
![\frac{3\pi}{4}= \frac{3*180}{4}=135^{\circ}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5Cpi%7D%7B4%7D%3D+%5Cfrac%7B3%2A180%7D%7B4%7D%3D135%5E%7B%5Ccirc%7D)
Ответ: 135°
<span>найти вершину параболы y=-(x+1)^2-4
координаты вершины
x0= -1
y0= -4
</span>