Xy = 8
x^2 + y^2 = 18
x = 8/y
(8/y)^2 + y^2 - 18 = 0
x = 8/y
64/y^2 + y^2 - 18 = 0*
*y^4 - 18y^2 + 64 = 0
Пусть y^2 = t, тогда
t^2 - 18t + 64 = 0
D = 324 - 256 = 68
t1 = ( 18 + 2√17)/2 = 9 + √17
t2 = (18 - 2√17)/2 = 9 - √17
Обратная замена
y^2 = 9 + √17
y = ± √(9 + √17)
y^2 = 9 - √17
y = ± √(9 - √17)
x₁ = 8/y = √(9 - √17)
y₁ = √(9 + √17)
x₂ = 8/y = - √(9 - √17)
y₂ = - √(9 + √17)
x₃ = 8/y = √(9 + √17)
y₃ = √(9 - √17)
x₄ = 8/y = - √(9 + √17)
y₄ = - √(9 - √17)