在等比数列an中，a5×a11=3,a5+a11=4则a12/a2=？

Question

如题所述

Answer 1

an = a1.q^(n-1)
a5.a11=3
(a1)^2.q^14=3 (1)
a5+a11 =4
a1q^4(1+q^6)=4 (2)
(2)^2/(1)
(1+q^6)^2/q^6 = 16/3
3(1+q^6)^2 =16q^6
3q^12-10q^6+3 =0
(3q^6-1)(q^6-3)=0
q^6 = 1/3 or 3
q^6 = 1/3 =>q^10 = (1/3)^(5/3)
q^6=3 => q^10 =3^(5/3)

a12/a2 = q^10 = (1/3)^(5/3) or 3^(5/3)

Answer 2

1、因为a5×a11=3
a5+a11=4
联立上述两式解方程得：a5=3或1；a11=1或3
2、由于an为等比数列，则an＝a1×q^（n-1)
所以a11/a5＝（a1*q^10）/（a1*q^4）＝q^6=1/3或3
所以q=(1/3)^(1/6)或3^(1/6)
3、a12/a2=（a1*q^11）/（a1*q）＝q^10=(1/3)^(10/6)或3^(10/6)
即：a12/a2＝q^10＝(1/3)^(5/3)或3^(5/3)

Answer 3

首先求a5和a11的值，a5=1，a11=3或a5=3，a11=1，设等比数列公比为q
a11/a5=q的6次幂=3或1/3，求出q
a12/a2=q的10次幂，代入q即可