Verified answer

x + y + xy = 11

xy(x + y) = 30

замена x + y = a  xy = b

a + b = 11

ab = 30

a = 11 - b

b(11 - b) = 30

b² - 11b + 30 = 0

D= 121 - 120 = 1

b12 = (11 +- 1)/2 = 5   6

1. b = 5 a = 11 - 5 = 6

x + y = 6

xy = 5

x = 6 - y

y(6 - y) = 5

y² - 6y + 5 = 0

D=36 - 20 = 16

y12=(6 +- 4)/2 = 1   5

y1 = 1   x1 = 5

y1 = 5   x1 = 1

1. b = 6 a = 11 - 6 = 5

x + y = 5

xy = 6

x = 5 - y

y(5 - y) = 6

y² - 5y + 6 = 0

D=25 - 24 = 1

y12=(5 +- 1)/2 = 2   3

y1 = 2   x1 = 3

y1 = 3   x1 = 2

ответ (2, 3) (3,2) (1,5) (5,1)