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问题 解答题
已知a+a-1=7，求下列各式的值：
（1）
a
3
2
-a-
3
2
a
1
2
-a-
1
2
； （2）a
1
2
+a-
1
2
； （3）a2-a-2
 &(a＞1)
．
答案

（1）

a
3
2
-a-
3
2
a
1
2
-a-
1
2
=
(a
1
2
)3-(a-
1
2
)3
a
1
2
-a-
1
2
=
(a
1
2
-a-
1
2
)(a+a-1+1)
a
1
2
-a-
1
2
=a+a-1+1=7+1=8．

（2）a+a-1=(a

1
2
+a-
1
2
)2-2a
1
2
•a-
1
2
=(a
1
2
+a-
1
2
)2-2=7；

∵a

1
2
+a-
1
2
＞0，

∴a

1
2
+a-
1
2
=3

（3）a+a-1=(a

1
2
-a-
1
2
)2+2a
1
2
•a-
1
2
=(a
1
2
-a-
1
2
)2+2=7

∵a＞1，

∴a

1
2
-a-
1
2
=
5
，

∴a-a-1=(a

1
2
+a-
1
2
)(a
1
2
-a-
1
2
)

=3

5
a2-a-2

=（a-a-1）（a+a-1）

=21

5
．

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