三个数1/a,1,1/c成等差数列,而三个数a^2,1,c^2成等比数列,求(a+c)/(a^2+c^2)写下过程~~

Question

三个数1/a,1,1/c成等差数列,而三个数a^2,1,c^2成等比数列,求(a+c)/(a^2+c^2)
写下过程~~

Answer 1

三个数1/a,1,1/c成等差数列,
1-1/a=1/c-1
2=1/a+1/c
a+c=2ac
a^2+2ac+c^2=4a^2c^2
a^2+c^2=4a^2c^2-2ac
三个数a^2,1,c^2成等比数列,
a^2/1=1/c^2
a^2c^2=1=(ac)^2
ac=1
a^2+c^2=4a^2c^2-2ac=4-2=2
(a+c)/(a^2+c^2)=2/2=1