решить системное уравнение

(3, 4) (4, 3) (11+2√31, 11-2√31) (11-2√31, 11+2√31)

xy(x-1)(y-1)=72

(x+1)(y+1)=20

xy(xy + 1 - (x+y)) = 72

xy + x+y + 1 = 20 x+y = 19 - xy

xy(xy + 1 - 19 + xy) = 72

2(xy)^2 - 18 xy - 72 = 0

(xy)^2 - 9xy - 36 = 0

D = 81 + 144 = 225

(xy)₁₂ = (9+-15)/2 = 12 -3

1. xy=12

(x-1)(y-1)=6

xy - x - y + 1 = 6

x+y=7

x=7-y

(7-y)y = 12

y^2-7y + 12=0

D=49 - 48 = 1

x=7-y y₁₂ = (7+-1)/2 = 3 4 x₁₂ = 4 3

2. xy = -3

(x-1)(y-1)=- 24

xy - x - y + 1 = -24

x+y = 25 + xy

x+y=22

x=22-y

(22-y)y = -3

y^2-22y - 3=0

D=484+ 12 = 496 y₃₄ = (22+-4√31)/2 = 11+-2√31 x₃₄ = 11-+2√31