(1)请从三个代数式4x2-y2,2xy+y2,4x2+4xy+y2中,任选两个构造一个分式,并化简该分式;(2)解方程:(x-1)2+2x-3=0.-数学

题目简介

(1)请从三个代数式4x2-y2,2xy+y2,4x2+4xy+y2中,任选两个构造一个分式,并化简该分式;(2)解方程:(x-1)2+2x-3=0.-数学

题目详情

(1)请从三个代数式4x2-y2,2xy+y2,4x2+4xy+y2中,任选两个构造一个分式,并化简该分式;
(2)解方程:(x-1)2+2x-3=0.
题型:解答题难度:中档来源:不详

答案

(1)本题答案不唯一.
4x2-y2
2xy+y2
(2分)
=
(2x+y)(2x-y)
y(2x+y)
(6分)
=class="stub"2x-y
y
(8分)
4x2-y2
4x2+4xy+y2
=
(2x+y)(2x-y)
(2x+y)2
=class="stub"2x-y
2x+y
y(2x+y)
(2x+y)(2x-y)
=class="stub"y
2x-y

2xy+y2
4x2-y2
=
y(2x+y)
(2x+y)(2x-y)
=class="stub"y
2x-y

2xy+y2
4x2+4xy+y2
=
y(2x+y)
(2x+y)2
=class="stub"y
2x+y

4x2+4xy+y2
4x2-y2
=
(2x+y)2
(2x+y)(2x-y)
=class="stub"2x+y
2x-y

4x2+4xy+y2
2xy+y2
=
(2x+y)2
y(2x+y)
=class="stub"2x+y
y


(2)x2-2x+1+2x-3=0(3分)
x2-2=0
x2=2(6分)
∴x1=
2
,x2=-
2
.(8分)

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