已知x2-8x+y2-y+161/4=0,求[(x+y)(x-y)-(x+y)2-2y(x-3y)]÷4y的值.

问题描述:

已知x2-8x+y2-y+16

1
4
=0,求[(x+y)(x-y)-(x+y)2-2y(x-3y)]÷4y的值.

x2-8x+y2-y+16

1
4
=0,
(x-4)2+(y-
1
2
2=0,
x-4=0,y-
1
2
=0,
x=4,y=
1
2

[(x+y)(x-y)-(x+y)2-2y(x-3y)]÷4y
=[x2-y2-x2-y2-2xy-2xy+6y2]÷4y
=[4y2-4xy]÷4y
=y-x
=
1
2
-4
=-3
1
2