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

D=25+24=49

cosx=6 - не подходит

cosx=-1  -> x=pi+2pi*k

cos2x-10cosx-11=02cos^2x-1-10cosx-11=02cos^2x-10cosx-12=0cos^2x-5cosx-6=0

x2 - 5x - 6 = 0D = b2 - 4acD = 25 + 24 = 49 = 7^2

x1,2 = -b ± √D/2ax1 = 5 + 7/2 = 12/2= 6x2 = 5 - 7/2 = - 2/2 = -1 x1 = 6; x2 = -1cosx=6 - (не удолт)cosx=-1 -> x=pi+2pi*k , к-N