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
=0,求[(x+y)(x-y)-(x+y)2-2y(x-3y)]÷4y的值. 1 4
答
x2-8x+y2-y+16
=0,1 4
(x-4)2+(y-
)2=0,1 2
x-4=0,y-
=0,1 2
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
=
-41 2
=-3
.1 2