已知3x²+xy-2y²=0(x≠0,y≠0),求x/y-y/x-x²+y²/xy的值

已知3x²+xy-2y²=0(x≠0,y≠0),求x/y-y/x-x²+y²/xy的值
已知3x²+xy-2y²=0(x≠0,y≠0),求x/y-y/x-x²+y²/xy的值

已知3x²+xy-2y²=0(x≠0,y≠0),求x/y-y/x-x²+y²/xy的值
3x²+xy-2y²=0(x≠0,y≠0),
3+y/x-2y^2/x^2=0,假设y/x=t
2t^2-t-3=0
(2t-3)(t+1)=0
t=3/2,t=-1
x/y-y/x-x²+y²/xy
(x^2-y^2-x^2-y^2)/(xy)
=-2y/x
=-2t
所以：
x/y-y/x-x²+y²/xy的值 3或2