Решите систему уравнений

{х+у+xy=1 {x^2y+хy^2=-30

xy = a

x + y = b

=> {a + b = 1

{ab = - 30

a² - a - 30 = 0

D = 1 + 120 = 121

a₁ = (1 - 11) / 2 = - 5; b₁ = 6

a₂ = 6; b₂ = - 5

{xy = - 5

{x + y = 6

x² - 6x - 5 = 0

D = 36 + 20 = 56

x₁ = (6 - 2√14) / 2 = 3 - √14; y₁ = 3 + √14

x₂ = 3 + √14; y₂ = 3 - √14

2) {xy = 6

{x+y = - 5

x² + 5x + 6 = 0

x₃ = - 2; y₃ = - 3

x₄ = - 3; y₄ = - 2

Ответ: (-2; - 3), (-3; - 2), (3 + √14; 3 - √14), (3 - √14; 3 + √14)