题目

实数1/a,1,1/c成等差数列实a^2,1,c^2成等比数列则（a+c）/（a^2 +c^2)=

提问时间：2020-08-02

答案

a^2,1,c^2成等比数列
a^2c^c=1
1/a,1,1/c成等差数列
2=1/a+1/c
(a+c)/ac=2
a+c=2ac
(a+c)/ac=2(平方）
[(a+c)/ac]^2=4
(a+c)^2/a^c^2=4
(a+c)^2=4a^c^2
(a+c)^2=4a^c^2
(a+c)^2=4
a+c=±2
当a+c=2时
(a+c)/(a^2 +c^2)
=(a+c)/[(a^2+2ac +c^2)-2ac]
=(a+c)/[(a+c)^2-(a+c)]
=2/[2^2-2]
=1
当a+c=-2时
(a+c)/(a^2 +c^2)
=(a+c)/[(a^2+2ac +c^2)-2ac]
=(a+c)/[(a+c)^2-(a+c)]
=-2/[(-2)^2-(-2)]
=-2/(4+2)
=-1/3