Решите уравнение: 8 cos² x - 10 cos x + 3 = 0.

Пусть y = cos x, тогда 8y² - 10y + 3 = 0

D = 100 - 4 * 8 * 3 = 100 - 96 = 4

y1 = (10 + √4) / (2 * 8) = (10 + 2) / 16 = 12/16 = 3/4

y2 = (10 - √4) / (2 * 8) = (10 - 2) / 16 = 8/16 = 1/2

cos x = 3/4 или cos x = 1/2

x = ±arccos(3/4) + 2πn или x = ±π/3 + 2πn, где n ∈ Z

Ответ: x = ±arccos(3/4) + 2πn, x = ±π/3 + 2πn, n ∈ Z