已知X²+Y²-8X-10Y+41=0,求Y/(X²-XY)+X/(Y²-XY)的值?

问题描述:

已知X²+Y²-8X-10Y+41=0,求Y/(X²-XY)+X/(Y²-XY)的值?

X²+Y²-8X-10Y+41=0
X²-8X+16+Y²-10Y+25=0
(x-4)²+(y-5)²=0
得x=4,y=5
Y/(X²-XY)+X/(Y²-XY)
=5/(-4)+4/(-4)
=-(9/4)