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