X^2-xy=12-y^2 x-2y=6 решите систему ..

  x^2-xy=12-y^2

  x-2y=6

  x^2-xy=12-y^2

  x=6+2y

(6+2y)^2-(6+2y)y=12-y^2

36+24y + 4y^2 - 6y - 2y^2 - 12 +y^2 = 0

3y^2 + 18y   +24 = 0

y^2 + 6y +8=0

y1 = -4

y2 = -2

x1=6+2*(-4)= -2

x2 = 6+2*(-2) = 2

x^2 - xy = 12 - y^2

x - 2y = 6

x^2 - xy = 12 - y^2

x = 6 + 2y

подставляем х.

(6 + 2y)^2 - y(6+2y) = 12 - y^2

x = 6 + 2y

36 + 24y + 4y^2 - 6y - 2y^2 - 12 + y^2 = 0

x = 6 + 2y

3y^2 + 18y + 24 = 0

выносим 3 за скобку:

3(y^2 + 6y + 8) = 0

y^2 + 6y + 8 = 0

d = 36 - 4*8 = 4 = 2^2

y1 = (-6 + 2) / 2 = -2

y2 = (-6 - 2) / 2 = -4

подставляем

y = -2

x = 6 - 4 = 2

y = -4

x = 6 - 8 = -2

ответ: (2 ; -2) и (-2 ; -4)

х=0.5       y=1/8

x=0.25     y=1/16

x=0.125   y=1/32