x^2+y^2+8x+10y+41=0
(x^2+8x+16)+(y^2+10y+25)=0
(x+4)^2+(y+5)^2=0
∴{x+4=0
y+5=0
解得{x=-4,y=-5
根号x分之y+根号y分之x
=√5/2+2√5/5
=9√5/10