√(y/x) - √(x/y) = 3/2
√(y/x) = a
a - 1/a = 3/2
2a² - 2 = 3a
2a² - 3a - 2 = 0
D = 9 + 16 = 5²
a₁ = 2; (a₂ = -0.5 не подходит)
√(y/x) = 2
y/x = 4 → y = 4x
Подстановка:
x + 4x + 4x² = 9
4x² + 5x - 9 = 0
D = 25 + 144 = 169
x₁ = 2 → y₁ = 8
x₂ = 1 → y₂ = 4
ОТВЕТ: (2; 8), (1; 4)