Question

若三个数1/a,1,1/c成等差数列,且三个数a^2,1,c^2成等比数列,则a+c/a^2+c^2=

Answer 1

这里,由1/a,1,1/c成等差数列求出a+c=2ac,由a^2,1,c^2成等比数列求出a^2c^2=1

a+c/a^2+c^2=a+c/（a+c）^2-2ac,如果ac=1,a+c/a^2+c^2=1,如果ac=-1,a+c/a^2+c^2=-1/3