Question

已知3x6^2+xy-2y^2=0，求y\x-x\y-xy\x^2+y^2的值

Answer 1

3x^2+xy-2y^2=0
(3x-y)(x+y)=0
3x=y,x=-y
x/y=1/3,x/y=-1

当x/y=1/3时，y/x=3
y/x-x/y-xy/(x^2+y^2)
=3-1/3-(xy/xy)/(x^2/xy+y^2/xy)
=8/3-1/(x/y+y/x)
=8/3-1/(1/3-3)
=8/3-1/(-8/3)
=8/3+3/8
=64/24+9/24
=73/24

当x/y=-1时，y/x=-1
y/x-x/y-xy/(x^2+y^2)
y/x-x/y-xy/(x^2+y^2)
=-1-(-1)-(xy/xy)/(x^2/xy+y^2/xy)
=-1/(x/y+y/x)
=-1/(-1-1)
=1/2