问题 填空题
已知a=
1
2+
3
,b=
1
2-
3
,则
a2-b2
2a-2b
=______.
答案

a=

1
2+
3
=
2-
3
(2+
3
)(2-
3
)
=2-
3

b=

1
2-
3
=
2+
3
(2-
3
)(2+
3
)
=2+
3

a2-b2
2a-2b
=
(a+b)(a-b)
2(a-b)
=
a+b
2
=
2-
3
+2+
3
2
=2.

故答案为:2

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