诺『An』是等比数列,An》0,且a2×a4＋2a3×a5＋a4×a6＝25,则a3＋a5等于
问题描述：
诺『An』是等比数列,An》0,且a2×a4＋2a3×a5＋a4×a6＝25,则a3＋a5等于
答
设a2=a,a3=aq,a4=aq^2,a5=aq^3,a6=aq^4
a2*a4+2a3*a5+a4*a6
=a*aq^2+2aq*aq^3+aq^2*aq^4
=a^2(q^2+2q^4+q^6)
=a^2*q^2(1+2q^2+q^4)
=(aq(1+q^2))^2
=(aq+aq^3))^2
=(a3+a5)^2
=25
又an＞0
所以
a3+a5=5
答
a2×a4＋2a3×a5＋a4×a6＝25
(a3+a5)^2=25
a3+a5=5