6 cos^2x + cos x - 1 = 0

Question

Математика

Алексий

30 октября, 09:07

6 cos^2x + cos x - 1 = 0

+2

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Маруха · Answer 1

6 cos²x + cosx - 1 = 0

cosx = t

6t² + t - 1 = 0

D = 1² + 4 * 6 * 1 = 1 + 24 = 25

t1 = (-1 + 5) / 2 * 6 = 4/12 = 1/3

t2 = (-1 - 5) / 2 * 6 = - 6/12 = - 1/2

cosx = - 1/2;

x = ±2/3π + 2πk;

cosx = 1/3;

x = arccos1/3 + 2πk;