Question

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)=

Answer 1

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