已知数列{An}满足A平方n+1=AnAn+2(nEN*),An〉0,且A2A4+2A3A5+A4A6=64,求a3+A5
问题描述:
已知数列{An}满足A平方n+1=AnAn+2(nEN*),An〉0,且A2A4+2A3A5+A4A6=64,求a3+A5
答
∵A²n+1=AnAn+2
∴A2A4+2A3A5+A4A6=A3²+2A3A5+A5²=(A3+A5)²=64
∵An>0 ∴A3+A5>0
∴A3+A5=8