Question

Ctg(pi*x)-ctg(pi*y)=-√(3); x-y=1/3; решите .

Answer 1

{ctg(pi x)-ctg(pi y) = -√(3), x-y = 1/3}
{ctg(pi x)+sqrt(3) = ctg(pi y), x = y+1/3}
{(sin(2 pi y))/(cos(2 pi y)-1)-(sin(2 pi x))/(cos(2 pi x)-1) = -√(3), x-y = 1/3}
x = n-1/2, y = n-5/6, n ∈ Z
x = n-1/6, y = n-1/2, n ∈ Z

Answer 2

X-y=1/3
sin(πx-πy)/sinπx*sinπy=-√3
sinπ(x-y)=-√3sinπxsinπy
-√3sinπxsinπy=sinπ/3=√3/2
sinπxsinπy=-1/2
1/2(cos(πx-πy)-cos(πx+πy))=-1/2
cosπ(x-y)-cosπ(x+y)=-1
cosπ/3-cosπ(x+y)=-1
cosπ(x+y)=1/2+1=3/2∉[-1;1] нет решения