X + y = 12
x^2/y + y^2/x = 18
x^3 + y^3 = 18xy
(x+y)(x^2-xy+y^2) = 18xy
12(x^2-xy+y^2) = 18xy
2x^2 - 2xy + 2y^2 - 3xy = 0
x^2 - 5/2xy + y^2 = 0
x^2 - (2 + 1/2)xy + (2 * 1/2)y^2 = 0
(x - 2y)*(x - y/2) = 0
x + y = 12, x = 2y -> x = 8, y = 4
x + y = 12, y = 2x -> x = 4, y = 8
ОДЗ
cosx≤0⇒x∈[π/2+2πn;3π/2+2πn,n∈z]
cosx=0⇒x=π/2+2πn,n∈z U x=3π/2+2πn,n∈z
tg²x+tgx=0
tgx(tgx+1)=0
tgx=0⇒x=πn,n∈z+ОДЗ⇒x=π+2πn,n∈Z
tgx=-1⇒x=-π/4+πn,n∈z +ОДЗ⇒x=3π/4+2πn,n∈z