问题 解答题
(1)设lg2=a,lg3=b,用a,b表示log512       (2)已知x
1
2
+x-
1
2
=3
,求
x2+x-2-2
x
3
2
+x-
3
2
-3
的值.
答案

(1)∵lg2=a,lg3=b,

log512=

lg12
lg5

=

lg3+2lg2
lg10-lg2

=

b+2a
1-a

(2)∵x

1
2
+x-
1
2
=3,

x2+x-2-2
x
3
2
+x-
3
2
-3

=

(x+x-1)2-4
(x
1
2
+x-
1
2
)(x-1 +x- 1) -3

=

[(x
1
2
+x-
1
2
)2-2]2-4
(x
1
2
+x-
1
2
)[(x
1
2
+x-
1
2
)2-3]-3

x

1
2
+x-
1
2
=3,

∴原式=

(32-2)2-4
3(32-3)-3
=3.

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