x^2+y^2-6x+4y+13=0
(x^2-6x+9)+(y^2+4y+4)=0
(x-3)^2+(y+2)^2=0
所以x=3,y=-2
所以
(2x-y)^2-2(2x-y)(x+2y)+(x+2y)^2
=[2x-y-(x+2y)]^2
=(x-3y)^2
=18
x^2+y^2-6x+4y+13=0
(x^2-6x+9)+(y^2+4y+4)=0
(x-3)^2+(y+2)^2=0
所以x=3,y=-2
所以
(2x-y)^2-2(2x-y)(x+2y)+(x+2y)^2
=[2x-y-(x+2y)]^2
=(x-3y)^2
=18