Question

xy(x-1)(y-1)=72
(x+1)(y+1)=20
Все это в системе.

Answer 1

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      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

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