Question

Помогите решить систему уравнений

Answer 1

xy - 4 = 7x/y  (1)

xy - 3/2 = y/2x  (2)

(2) - (1)

4 - 3/2 = y/2x - 7x/y

x/y = t

5/2 = 1/2t - 7t

5t = 1 - 14t²

14t² + 5t - 1 = 0

D = 25 + 4*14 = 81

t12=(-5 +- 9)/28 = -1/2    1/7

1. x/y = -1/2

y = -2x

x*(-2x) - 4 = 7*(-1/2)

-2x² = 1/2

решений нет

2. x/y = 1/7

y =7x

x*7x - 4 = 7*1/7

7x² = 5

x² = 5/7

x = √5/7  y = 7√5/7

x = -√5/7  y = -7√5/7