Question

Помогите решить
Cos²x+5cosx=6

Answer 1

Ответ:

x = +- (π-arccos(6)) + 2πk , k € Z

x = 2πk , k € Z

Объяснение:

${ \cos }^{2}x + 5 \cos(x) = 6 \\ { \cos }^{2}x + 5 \cos(x) - 6 = 0$

Замена cos x = a

a^2 + 5a - 6 = 0

D = (b^2) - 4ac = (5^2) - 4 × 1 × (-6) = 25 + 24 = 49 > 0 , 2 корня

x1 = ((-b) - √D / 2a ) = ((-5) - √49 / 2 × 1 ) = ((-5) - 7 / 2 ) = -12/2 = -6

x2 = ((-b) + √D / 2a ) = ((-5) + √49 / 2 ) = ((-5) + 7 / 2 ) = 2/2 = 1

cos x = -6

x = +- arccos(-6) + 2πk , k € Z

x = +- (π-arccos(6)) + 2πk , k € Z

cos x = 1

x = 2πk , k € Z