Решить систему (x+3/y-3 + y-3/x+3 = 17/4(xy=4

Замена (x+3)/(y-3) = t
t + 1/t = 17/4
xy = 4
Решаем 1 уравнение
4t^2 - 17t + 4 = 0
(t - 4)(4t - 1) = 0

1) t1 = (x+3)/(y-3) = 4
x + 3 = 4(y - 3)
xy = 4
Подставляем 1 уравнение во 2 уравнение
x = 4y - 12 - 3 = 4y - 15
(4y - 15)*y = 4
4y^2 - 15y - 4 = 0
(y - 4)(4y+ 1) = 0
y1 = 4; x1 = 4/y = 1
y2 = -1/4; x2 = 4/y = -16

2) t2 = (x+3)/(y-3) = 1/4
4(x + 3) = y - 3
xy = 4
Подставляем 1 уравнение во 2 уравнение
y = 4(x + 3) + 3 = 4x + 12 + 3 = 4x + 15
x(4x + 15) = 4
4x^2 + 15x - 4 = 0
(x - 4)(4x + 1) = 0
x3 = 4; y3 = 4/x = 1
x4 = -1/4; y = 4/x = -16
Ответ: (1; 4); (-16; -1/4); (4; 1); (-1/4; -16)