Замена y=x² +x
y(y-5)=84
y² -5y-84=0
D=25+336=361
y₁=(5-19)/2= -7
y₂=(5+19)/2=12
При у= -7
x² +x= -7
x² +x+7=0
D=1-28<0
нет решений.
При у=12
x² +x=12
x² +x-12=0
D=1+48=49
x₁ = (-1-7)/2= -4
x₂ = (-1+7)/2=3
Ответ: -4; 3.
![\sin 2x+\sqrt{3}\sin x-2\cos x=\sqrt{3}\\ 2\sin x\cos x+\sqrt{3}\sin x-2\cos x-\sqrt{3}=0\\ \sin x(2\cos x+\sqrt{3})-(2\cos x+\sqrt{3})=0\\ (2\cos x+\sqrt{3})(\sin x-1)=0](https://tex.z-dn.net/?f=%5Csin+2x%2B%5Csqrt%7B3%7D%5Csin+x-2%5Ccos+x%3D%5Csqrt%7B3%7D%5C%5C+2%5Csin+x%5Ccos+x%2B%5Csqrt%7B3%7D%5Csin+x-2%5Ccos+x-%5Csqrt%7B3%7D%3D0%5C%5C+%5Csin+x%282%5Ccos+x%2B%5Csqrt%7B3%7D%29-%282%5Ccos+x%2B%5Csqrt%7B3%7D%29%3D0%5C%5C+%282%5Ccos+x%2B%5Csqrt%7B3%7D%29%28%5Csin+x-1%29%3D0)
Произведение равно нулю, если хотя бы один из множителей равен 0
![2\cos x+\sqrt{3}=0\\ \cos x=-\frac{\sqrt{3}}{2}~~~\Leftrightarrow~~~~ \boxed{x_1=\pm\frac{5\pi}{6}+2\pi n,n \in \mathbb{Z}}\\ \\ \\ \sin x-1=0\\ \\ \sin x=1~~~\Leftrightarrow~~~~ \boxed{x_2=\frac{\pi}{2}+2\pi k,k \in \mathbb{Z}}](https://tex.z-dn.net/?f=2%5Ccos+x%2B%5Csqrt%7B3%7D%3D0%5C%5C+%5Ccos+x%3D-%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D~~~%5CLeftrightarrow~~~~+%5Cboxed%7Bx_1%3D%5Cpm%5Cfrac%7B5%5Cpi%7D%7B6%7D%2B2%5Cpi+n%2Cn+%5Cin+%5Cmathbb%7BZ%7D%7D%5C%5C+%5C%5C+%5C%5C+%5Csin+x-1%3D0%5C%5C+%5C%5C+%5Csin+x%3D1~~~%5CLeftrightarrow~~~~+%5Cboxed%7Bx_2%3D%5Cfrac%7B%5Cpi%7D%7B2%7D%2B2%5Cpi+k%2Ck+%5Cin+%5Cmathbb%7BZ%7D%7D)