试题

题目:
已知x=
2
+1
y=
2
-1
,试求
x2-y2
x2+2xy+y2
的值.
答案
解:因为x=
2
+1
y=
2
-1

所以
x2-y2
x2+2xy+y2
=
(x+y)×(x-y)
(x+y)2
=
x-y
x+y
=
2
2
2
=
2
2

所以答案为
2
2

解:因为x=
2
+1
y=
2
-1

所以
x2-y2
x2+2xy+y2
=
(x+y)×(x-y)
(x+y)2
=
x-y
x+y
=
2
2
2
=
2
2

所以答案为
2
2
考点梳理
二次根式的化简求值.
此题化简原式后可得
x2-y2
x2+2xy+y2
=
(x+y)×(x-y)
(x+y)2
=
x-y
x+y
,代入即可.
把原式化简后再代入,此题较为简单.
计算题.
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