在正项等比数列{a(n)}中,a1a5+2a3a5=a3a7=25,则a3+a5=?
问题描述:
在正项等比数列{a(n)}中,a1a5+2a3a5=a3a7=25,则a3+a5=?
答
因为{a(n)}是正项等比数列,则有a3>0,a5>0.(an>0)
an*an=a(n-1)*a(n+1).
则a1a5+2a3a5=a3*a3+2a3a5=25,a3a7=a5*a5=25.有a5=5.(a5=-5舍去)
a3*a3+10a3=25.解得a3=(5√2)-5.(-5-5√2舍去)
则a3+a5=5√2
答
a1a5+2a3a5+a3a7=(a3)^2+2a3a5+(a5)^2=(a3+a5)^2=25
正项等比数列
a3+a5=5