设公差为非零的等差数列{An}与等比数列{Bn},满足A1=B1,A3=B3,A7=B5,求公比q

A1=B1,A3=B3,A7=B5
a1+2d=b1*q^2
a1+6d=b1*q^4
2d=b1*(q^2-1)
6d=b1*(q^4-1)
1/3=1/(q^2+1)
q=±√2

A1=B1，A1+2d=B1*q*q，A1+6d=B1*q*q*q*q
等价于（令A1=B1=a）
（q*q-1）a=2d............1
6d=(q*q*q*q-1)a...........2
2式除三带入一式，得
q*q*q*q+3q*q-4=0
即
q=±√2