求一道数学题解!已知：x²+y²-8x-10y+41=0,求x/y-y/x=?

求一道数学题解!已知：x²+y²-8x-10y+41=0,求x/y-y/x=?
求一道数学题解!
已知：x²+y²-8x-10y+41=0,求x/y-y/x=?

求一道数学题解!已知：x²+y²-8x-10y+41=0,求x/y-y/x=?
x²+y²-8x-10y+41=0
x²-8x+16+y²-10y+25=0
(x-4)²+(y-5)²=0
∴x-4=0
y-5=0
∴x=4
y=5
∴x/y-y/x
=4/5 -5/4
=-9/20

x^2+y^2-8x-10y+41=0x^2-8x+16+y^2-10y+25=0(x-4)^2+(y-5)^2=0x-4=0 y-5=0x=4 y=5x/y-y/x=4/5-5/4=0.8-1.25=-0.45