等比数列{an},a2+a5=36,a1*a6=128,则a8=
问题描述：
等比数列{an},a2+a5=36,a1*a6=128,则a8=
答
等比数列{an},a2+a5=36,a1*a6=128,则a8=
好简单的啊
a1*q+a1*q^4=36 ---> a1*(q+q^4)=36 -->a1=36/(q+q^4)
a1*a1*q^5=128 ---->36^2/(q+q^4)^2 *q^5=128
a8=a1*q^7
答
等比则a2a5=a1a6=128a2+a5=36由韦达定理a2和a5是方程x²-36x+128=0的根(x-4)(x-32)=0x=4,x=32a2=4,a5=32则q²=a5/a2=8q=2a1=a2/q=2a8=a1*q^7=256a2=32,a5=4则q²=a5/a2=1/8q=1/2a1=a2/q=64a8=a1*q^7=1/2...