Question

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

Answer 1

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