3sin^2x+ cos^2x=5cosx

Question

3sin^2x+ cos^2x=5cosx

Answer 1

3(1-cos^2 x)+cos^2 x-5cos^2 x=0
3-3cos^2 x+cos^2 x-5cos x=0
-2cos^2 x-5cos x+3=0
2cos^2 x+5cos x-3=0
cosx=t
2t^2+5t-3=0
D=25+4*2*3=49
t=-5+7)/4=1/2
t2=-5-7)/4=-3
-3-посторонний корень
cosx=1/2.  x=π/3+2πn.  x=-π/3+2πk.n.k∈Z