Question

Помогите решить уравнение $cos(x^{2} +x)+cos(x+\frac{2\pi }{3} )+cos(x+\frac{4\pi }{3} )=0$

Answer 1

cos(x²+x)+ cos(x+2π/3)+cos(x+4π/3)=0

cos(x+2π/3)+cos(x+4π/3)=2 cos(x+π)*cos(π/3)=-cosx

cos(x²+x)-cosx=0

-2sin(x²/2+x)*sin(x²/2)=0

x²/2+x=πn; n∈Z;x²+2x-2πn=0; х=-1±√(1+2πn); n∈Z;

x²/2=πк. к∈Z; х=±√(2πк). к∈Z;