Question

Решите систему уравнений
Х^2+у^2=2
Ху=1

Answer 1

x = 1/y = y^(-1)
y^(-2) + y^2 = 2
y^4 - 2y^2 + 1 = 0
D = 4 - 4 = 0
y^2 = 2/2 = 1
y1 = -1, x1 = -1
y2 = 1, x2 = 1