Реши уравнение: 5y2+15y−(y+3)=0 корни уравнения y1= ,y2=

Question

Алгебра: Реши уравнение: 5y2+15y−(y+3)=0 корни уравнения y1= ,y2=

polyzaicka · Accepted Answer

F(x) = cos5x · cos(x + π/6)
g(x) = sin5x · sin(x + π/6) + 0.5√3
cos5x · cos(x + π/6) = sin5x · sin(x + π/6) + 0.5√3
cos5x · cos(x + π/6) - sin5x · sin(x + π/6) = 0.5√3
cos (6x + π/6) = 0.5√3
6x + π/6 = ⁺₋ π/6 + 2πn    n∈Z
1) 6x₁ + π/6 = + π/6 + 2πn    n∈Z 2) 6x₂ + π/6 = - π/6 + 2πn    n∈Z
1) 6x₁ = 2πn    n∈Z    2) 6x₂ = - π/3 + 2πn    n∈Z
1) x₁ = πn/3    n∈Z    2) x₂ = - π/18 + πn/3    n∈Z
ответ: x₁ = πn/3    n∈Z
x₂ = - π/18 + πn/3    n∈Z

MOGZ ответил