Question

Решить уравнение. 2cos^2x - cosx - 1 = 0

Answer 1

$\displaystyle 2cos^2x-cosx-1=0\\\\cosx=t; |t| \leq 1\\\\2t^2-t-1=0\\\\D=1+8=9\\\\t_{1.2}= \frac{1\pm 3}{4}\\\\t_1=1; t_2=- \frac{1}{2}$

$\displaystyle cosx=1; x=2 \pi n; n\in Z\\\\cosx=- \frac{1}{2}; x=\pm \frac{2 \pi }{3}+2 \pi k; k\in Z$