Question

$1+2sin frac{ pi x}{3}=0$ если х (2; 4)

Answer 1

1+2sin(πx/3)=0
2sin(πx/3)=-1
sin(πx/3)=-1/2
πx/3=(-1)^n *arcsin(-1/2)+πn, n∈Z
πx/3=(-1)^(n+1) *(π/6)+πn, n∈Z |:(π/3)
x=(-1)^(n+1) *(1/2)+3n, n∈Z
n=0. x=(-1)¹ *(1/2)+3*0. x=1/2 ∉(2;4)
n=1. x=(-1)²*(1/2)+3*1. x=3,5
n=2. x=(-1)³ *(1/2)+3*2. x=5?5∉(2;4)
ответ: х=3,5