Question

.若等比数列{an}中,a3a9=1,a1a5+a8a10=8,求a3+a9

在线等~~~~~~快呀

Answer 1

由等比中项性质得：a1·a5=a3² a8·a10=a9²
a1·a5+a8·a10=8
a3²+a9²=8
(a3+a9)²=a3²+a9²+2·a3·a9
=8+2·1
=10
a3+a9=√10或a3+a9=-√10

Answer 2

a3+a9=√10

过程：∵在等比数列中
a1a5+ a8a10=8
∴a3^2+a9^2=8
(a3+a9)^2 - 2a3a9=8
(a3+a9)^2=8+2*1=10
a3+a9=√10