решить уравнение cos2x-10cosx-11=0

cos2x-10cosx-11=0

2cos^2x-1-10cosx-11=0

2cos^2x-10cosx-12=0

cos^2x-5cosx-6=0

x2 - 5x - 6 = 0

D = b2 - 4ac

D = 25 + 24 = 49 = 7^2

x1,2 = - b ± √D/2a

x1 = 5 + 7/2 = 12/2 = 6

x2 = 5 - 7/2 = - 2/2 = - 1

x1 = 6; x2 = - 1

cosx=6 - (не удолт)

cosx=-1 - > x=pi+2pi*k, к-N

cos2x-10cosx-11=0

2cos^2x-1-10cosx-11=0

2cos^2x-10cosx-12=0

cos^2x-5cosx-6=0

D=25+24=49

cosx=6 - не подходит

cosx=-1 - > x=pi+2pi*k