Question

Пожалуйста, даю 30 балов!
Решить уравнение
5cos14x+cos7x-4=0

Answer 1

$5cos14x+cos7x-4 = 0\cos14x = cos^2 7x - sin^2 7x = cos^2 7x - 1 + cos^2 7x = 2cos^2 7x - 1\10cos^2 7x - 5 + cos 7x - 4 = 10cos^2 7x +cos7x - 9 = 0\D = 1 + 4cdot9cdot10 = 361\cos_1 7x = frac{-1 + 19}{20} = frac{9}{10}\cos_2 7x = frac{-1 - 19}{20} = -1\cos_1 7x = frac9{10} Rightarrow x = frac17cdotarccosfrac9{10}\cos_2 7x = -1 Rightarrow x = frac17cdot(pi + pi k)$