x²+y²-2x-6y+10=0 求分式x²-y²/xy

把10拆成1+9
(x²-2x+1)+(y²-6y+9)=0
(x-1)²+(y-3)²=0
平方大于等于0
相加为0则都等于0
所以x-1=0,y-3=0
x=1,y=3
所以原式=(1²-3²)/(1×3)=-8/3

x²+y²-2x-6y+10=0
x²-2x+1+y²-6y+9=0
(x-1)²+(y-3)²=0
x-1=0 y-3=0
x=1 y=3
x²-y²/xy=1²-3²/1*3=-8/3

x²+y²-2x-6y+10=0
(x-1)²+(y-3)²=0
x=1,y=3

x²-y²/xy=1-9/3=-2