等比等差數學問題

4, a, b 成等比數列 => a = 4r ... (1)
b = 4r^2 ... (2)
b, c, 64 成等比數列 => c = bR ... (3)
64 = bR^2 ... (4)
(2)及(3) => c = 4r^2R
(2)及(4) => 64 = 4r^2R^2
rR = +/-4
a, b, c 成等差數列 => (a + c)/2 = b
(4r + 4r^2R)/2 = 4r^2
1 + rR = 2r
若rR = 4 => r = 5/2 => R = 8/5 => a = 10, b = 25, c = 40
若rR = -4 => r = -3/2 => R = 8/3 => a = -6, b = 9, c = 24

2009-11-21 19:22:51 補充：
起初我也是用筱紫的方法,但發覺要考慮甚麼情況合適甚麼情況不合適,比較麻煩,改用現有方法,就沒有了這樣的麻煩了.

4與64之間插入a,b,c 三數 使
4, a, b 成等 比數列----->a^2=4b..........(1)
b, c, 64成等比數列,---->c^2=64b........(2)
a, b, c 成等差數列------>2b=a+c........(3)

16a^2=c^2, c=+-4a(負不合,
c=4a, 代入(3)b=5/2a, a:b:c=2:5:8
令a=2r, b=5r, c=8r 代入(1)
4r^2=20r, r=5, 0(不合, 公比不為0)
三數為10,25,40

c=-4a, 代入(3)b=-3/2a, a:b:c=2:-3:-8
令a=2r, b=-3r, c=-8r 代入(1)
4r^2=-12r, r=-3, 0(不合, 公比不為0)
三數為-6,9,24