以知X．X+Y．Y－8X－10Y+41＝0,求 X／｛Y．Y－XY｝+Y／｛X．X－XY｝的值．

题目

以知X．X+Y．Y－8X－10Y+41＝0,求 X／｛Y．Y－XY｝+Y／｛X．X－XY｝的值．
怎么做啊?

答案

x²+y²-8x-10y+41=0
(x-4)²+(y-5)²=0
x-4=0得x=4,y-5=0得y=5
x/(y²-xy)+y/(x²-xy)
=x/y(y-x)+y/x(x-y)
=x²/xy(y-x)-y²/xy(y-x)
=(x²-y²)/xy(y-x)
=-(x+y)(x-y)/xy(x-y)
=-(x+y)/(xy)
=-(4+5)/(4·5)
=-9/20