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

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

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)

X²+Y²-8X-10Y+41=0
(X²-8X+16)+(Y²-10Y+25)=0
(X-4)²+(Y-5)²=0
X=4;Y=5
Y/(X²-XY)+X/(Y²-XY)
=Y/X(X-Y)-X/Y(X-Y)
=(Y²-X²)/XY(X-Y)
=-(X+Y)/XY
=-9/20