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...