问题 解答题
计算下列各式:
(1)
(a
2
3
b-1)
-,
1
2
a
1
2
b
1
3
6a•b5

(2)2(lg
2
)2+lg
2
•lg5+
(lg
2
)
2
-lg2+1
答案

(1)

(a
2
3
b-1)
-,
1
2
a
1
2
b
1
3
6a•b5
=
a-
1
3
b
1
2
a
1
2
•b
1
3
a
1
6
b
5
6
=
a
1
6
b
5
6
a
1
6
b
5
6
=1

(2)2(lg

2
)2+lg
2
•lg5+
(lg
2
)
2
-lg2+1

=2(lg2

1
2
2+lg2
1
2
•lg5+
(lg2
1
2
)2-lg2+1

=2(

1
2
lg2)2+
1
2
lg2•lg5+
(
1
2
lg2)2-lg2+1

=2(

1
2
lg2)2+
1
2
lg2•lg5+
(
1
2
lg2-1)2

=

1
2
lg2(lg2+lg5)+|
1
2
lg2-1|

=

1
2
lg2•lg(2•5)+1-
1
2
lg2

=

1
2
lg2+1-
1
2
lg2=1

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