问题 解答题
(1)若x
1
2
+x-
1
2
=3
,求
x
3
2
+x-
3
2
-3
x2+x-2-2
的值;
(2)化简
a3b2
3ab2
(a
1
4
b
1
2
)
4
3
b
a
(a>0,b>0).
答案

(1)∵x

1
2
+x-
1
2
=3,

∴x+x-1=9-2=7,

x2+x-2=49-2=47,

x

3
2
+x-
3
2
=(x
1
2
+x-
1
2
)(x+x-1-1)
=3×6=18,

x
3
2
+x-
3
2
-3
x2+x-2-2
=
18-3
47-2
=
1
3

(2)∵a>0,b>0,

a3b2
3ab2
(a
1
4
b
1
2
)
4
3
b
a

=

a
3
2
b•[(ab2)
1
3
]
1
2
ab2(
b
a
)
1
3

=

a
3
2
b•a
1
6
b
1
3
a
2
3
b
7
3

=

a
10
6
b
4
3
a
2
3
b
7
3

=

a
b

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