5-5cos^2x+8cosx+1=cosx+cos^2x
6cos^2x-7cosx-6=0
6t^2-7t-6=0 t>=0 -1<=t<=1
решений нет
6t^2-9t-6=0
2t^2-3t-2=0
t<0
t=-1/2
cosx=-1/2
x=2П/3+2Пk
x=4П/3+2Пk
5-5cos^2x+8cosx+1=cosx+cos^2x
6cos^2x-7cosx-6=0
6t^2-7t-6=0 t>=0 -1<=t<=1
решений нет
6t^2-9t-6=0
2t^2-3t-2=0
t<0
t=-1/2
cosx=-1/2
x=2П/3+2Пk
x=4П/3+2Пk