已知1是a2与b2的等比中项,又是1a与1b的等差中项,则a+ba2+b2的值是()A.1或12B.1或-12C.1或13D.1或-13-数学

题目简介

已知1是a2与b2的等比中项,又是1a与1b的等差中项,则a+ba2+b2的值是()A.1或12B.1或-12C.1或13D.1或-13-数学

题目详情

已知1是a2与b2的等比中项,又是
1
a
1
b
的等差中项,则
a+b
a2+b2
的值是(  )
A.1或
1
2
B.1或-
1
2
C.1或
1
3
D.1或-
1
3
题型:单选题难度:偏易来源:不详

答案

∵1是class="stub"1
a
class="stub"1
b
的等差中项
class="stub"1
a
+class="stub"1
b
=class="stub"a+b
ab
=2,即a+b=2ab,
∵1是a2与b2的等比中项,
∴ab=±1
class="stub"a+b
a2+b2
=class="stub"a+b
(a+b)2-2ab
=class="stub"2ab
4a2b2-2ab
=1或-class="stub"1
3

故选D

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