Question

已知x^2-2x+y^2+6y+10=0,求分式x^2-2xy/xy+y^2的值

Answer 1

x^2-2x+y^2+6y+10=0,

x^2-2x+1+y^2+6y+9=0,

(x-1)²+(y+3)²=0

∴x-1=0

y+3=0

∴x=1

y=-3

∴(x^2-2xy)/(xy+y^2)=(1+6)/(-3+9)=7/6