Question

三个互不相等的实数a,b,c成等差数列,且a,c,b成等比数列,则a:b:c=

Answer 1

因为是等差数列，可以设b=a+d，c=a+2d
而a，c，b成等比数列
c^2=ab
(a+2d)(a+2d)=a(a+d)
a=-4/3*d
b=-1/3*d
c=2/3*d
则a：b：c=4:1:(-2)

Answer 2

a+c=2b.......(1)
a=2b-c........(2)
ab=c²..........(3)
(3)/(2)： b=c²/(2b-c)
2b²-bc=c²
2(b/c)²-b/c=1
2[(b/c)-1/4]²=1+1/8
b/c-1/4=±3/4
b/c=(1±3)/4
∵b≠c
∴b/c=(1-3)/4=-1/2
b=-c/2
代入(2)： a=2(-c/2)-c
a=-2c
a:b:c=(-2c):(-c/2):c
=(-2):(-1/2):1
=4:1:(-2)