система срочноx+y=xyx^2+y^2=4xy

x+y = xy
x + y = 4xy

x+y = xy
x + y + 2xy = 6xy

x+y = xy
(x+y) = 6xy

x+y=xy
xy = 6xy

x+y = xy
xy(xy-6) = 0

x+y = xy
x = 0 либо y = 0 или xy= 6
1) x = 0 =gt; y = 0 - 1-ый ответ
2) xy = 6

x+y = 6
x + y = 24

y = 6-x
x + 36 - 12x + x = 24

y = 6-x
2x - 12x + 12 = 0

x - 6x + 6 = 0
D = 36 - 24 = 12
x1 = (6-23)/2 = 3-3 =gt; y1 = 3 + 3
x2 = 3+3 =gt; y2 = 3-3

Ответ: (0; 0); (3-3; 3+3); (3+3; 3-3)

X^2+2xy+y^2=6xy
(x+y)^2=6xy
(xy)^2=6xy
xy(xy-6)=0
1) xy=0
x+y=xy
x+y=0
xy=0
x=0
y=0
2) xy=6
x+y=xy
x+y=6
x=6-y
(6-y)y=6
y^2-6y+6=0
D=12
y1=(6+2sqrt(3))/2=3+sqrt(3)
y2=3-sqrt(3)
x1=6-3-sqrt(3)=3-sqrt(3)
x2=6-3+sqrt(3)=3+sqrt(3)
Ответ: (0;0), (3-sqrt(3);3+sqrt(3)), (3+sqrt(3);3-sqrt(3))