已知[(x2+y2)-(x-y)2+2y(x-y)]÷4y=1,求4x4x2-y2-12x+y的值.-数学

题目简介

已知[(x2+y2)-(x-y)2+2y(x-y)]÷4y=1,求4x4x2-y2-12x+y的值.-数学

题目详情

已知[(x2+y2)-(x-y)2+2y(x-y)]÷4y=1,求
4x
4x2-y2
-
1
2x+y
的值.
题型:解答题难度:中档来源:襄阳

答案

[(x2+y2)-(x-y)2+2y(x-y)]÷4y
=(x2+y2-x2+2xy-y2+2xy-2y2)÷4y
=(4xy-2y2)÷4y
=x-class="stub"1
2
y
∵x-class="stub"1
2
y=1,
∴2x-y=2,
class="stub"4x
4x2-y2
-class="stub"1
2x+y

=class="stub"4x
(2x+y)(2x-y)
-class="stub"1
2x+y

=class="stub"4x-2x+y
(2x+y)(2x-y)

=class="stub"2x+y
(2x+y)(2x-y)

=class="stub"1
2x-y

=class="stub"1
2

更多内容推荐