Question

2cos^2x+14 cosx=3 sin^2x нужно решить уровнение

Answer 1

$2cos^{2}x+14cosx=3sin^{2}x \ 2cos^{2}x+14cosx-3sin^{2}x=0 \ 2cos^{2}x+14cosx-3(1-cos^{2}x)=0\2cos^{2}x+14cosx-3+3cos^{2}x=0\5cos^{2}x+14cosx-3=0\cosx=t\5t^{2}+14t-3=0\D=196+60=256\x_{1}= frac{-14+16}{10}=0,2 \ x_{2}= frac{-14-16}{10}=-3 \ cosx neq -3 \ cosx=0,2\x_{1}=arccos frac{1}{5}+2 pi n\x_{1}=-arccos frac{1}{5}+2 pi n$