xy + 1/x + 1/y = 8 => 1/x + 1/y = 8 - xy
=> (x+y)/xy = 8 - xy 知 x + y = 12
于是 12/xy = 8 - xy 令 xy=T 可得 T=6或T=2
再联立 x + y = 12 ,xy = 2
x=6±√(34) y=6减加根号34
x + y = 12 ,xy = 6
x=6±√(30) y=6减加根号30