-.-
a1+a2+a3=7
a1^2+a2^2+a3^2=99
所以有 a2(1/q+1+q)=7 ①
a2^2(1/q^2+1+q^2)=99 ②
(a1+a2+a3)^2=49=a1^2+a2^2+a3^2+2a1a2+2a1a3+2a2a3
-50=2(a1a2+a1a3+a2a3)
a1a2+a1a3+a2a3=-25 → a2^2(1+q+1/q)=-25
①^2/② → (1+q^2+1/q^2+2/q+2q+2)/(1/q^2+1+q^2)=49/99
50(q^2+1/q^2)+198(q+1/q)+248=0
令q+1/q=t 所以 q^2+1/q^2=t^2-2
所以有 50(t^2-2)+198t+248=0
50t^2+198t+148=0 t=-1 或者t=-2.96
q+1/q=-1 (舍) or -2.96
1+q+1/q=-1.96 a2^2=625/49 a2=25/7 or -25/7
得到 q=（37+2√186)/25 or (37-2√186)/25
(a1,a2,a3)=((37-2√186)/7,25/7,(37+2√186)/7)
or ((37+2√186)/7,25/7,(37-2√186)/7)
or (-(37+2√186)/7,-25/7,-(37-2√186)/7)
or (-(37-2√186)/7,-25/7,-(37+2√186)/7）