已知[(x2+y2)-(x-y)2+2y(x-y)]÷4y=1,求4x/4x2−y2-1/2x+y的值.
问题描述:
已知[(x2+y2)-(x-y)2+2y(x-y)]÷4y=1,求
-4x 4x2−y2
的值. 1 2x+y
答
[(x2+y2)-(x-y)2+2y(x-y)]÷4y
=(x2+y2-x2+2xy-y2+2xy-2y2)÷4y
=(4xy-2y2)÷4y
=x-
y1 2
∵x-
y=1,1 2
∴2x-y=2,
∴
-4x 4x2−y2
,1 2x+y
=
-4x (2x+y)(2x−y)
1 2x+y
=
4x−2x+y (2x+y)(2x−y)
=
2x+y (2x+y)(2x−y)
=
1 2x−y
=
.1 2