Question

若x2+y2-8x-10y+41=0 那么x/y+y/x=?

Answer 1

x�0�5+y�0�5-8x-10y+41=0
(x�0�5-8x+16)+(y�0�5-10y+25)=0
(x-4)�0�5+(y-5)�0�5=0
x-4=0,y-5=0
x=4,y=5
x/y-y/x
=4/5-5/4
=-9/20

Answer 2

解： x2+y2-8x-10y+41=0 拆项配方 （x-4)^2+(y-5)^2=0 x=4, y=5 x/y+y/x=4/5+5/4=41/20

Answer 3

方程可以配成平方和式子：(x-4)平方+(y-5)平方=0，很显然x=4,y=5！所以所求式等于：4/5+5/4=2！