(1)已知x12+x-12=3,求x+1x的值;(2)求值:(log43+log83)•(log32+log98)-数学

题目简介

(1)已知x12+x-12=3,求x+1x的值;(2)求值:(log43+log83)•(log32+log98)-数学

题目详情

(1)已知x
1
2
+x
1
2
=3,求x+
1
x
的值; 
(2)求值:(log43+log83)•(log32+log98)
题型:解答题难度:中档来源:不详

答案

(1)∵xclass="stub"1
2
+x-class="stub"1
2
=3,
(xclass="stub"1
2
+x-class="stub"1
2
)2=9

∴x+x-1+2=9,
x+class="stub"1
x
=7

(2)(log43+log83)•(log32+log98)
=(
log23
log24
+
log23
log28
)
×(log32+
log38
log39
)

=(
log23
2
+
log23
3
)
×(log32+
3log32
2
)

=log23×log32×(class="stub"1
2
+class="stub"1
3
)(1+class="stub"3
2
)

=1×class="stub"5
6
×class="stub"5
2

=class="stub"25
12

更多内容推荐