{an}是等比数列,且an>0,a2a4+2a3a5+a4a6=25,则a3+a5等于?

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{an}是等比数列,且an>0,a2a4+2a3a5+a4a6=25,则a3+a5等于?
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{an}是等比数列,且an>0,a2a4+2a3a5+a4a6=25,则a3+a5等于?
{an}是等比数列,且an>0,a2a4+2a3a5+a4a6=25,则a3+a5等于?

{an}是等比数列,且an>0,a2a4+2a3a5+a4a6=25,则a3+a5等于?
因为是等比数列,所以(a3)^2=a2乘以a4,(a5)^2=a4乘以a6,所以a2a4+2a3a5+a4a6=25,即(a3)^2+2a3a5+(a5)^2=25,即(a3+a5)^2=25,因为an>0,所以a3+a5=5

a2a4=a3^2
a4a6=a5^2
a3^2+2a3a5+a5^2=(a3+a5)^2=25 so a3+a5=5