If a,b,c and d are in continued proportion, show that (a-b):(a+b)=(a-d):(a+2b+2c+d)
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if a,b,c,d are in continued proportion, prove that
(a+b)(b+c)-(a+c)(b+d)=(b-c)^2.
Sorry, but that isn't true, for here is a counter-example:
For a,b,c,and d to be in continued proportion,
a:b = b:c = c:d
3:9 = 9:27 = 27:81
Let a=3, b=9, c=27, d=81
(a+b)(b+c)-(a+c)(b+d)≟(b-c)�
(3+9)(9+27)-(3+27)(9+81)≟(9-27)�
(12)(36)-(30)(90)≟(-18)�
432 - 2700 ≟ 324
-2268 ≠ 324
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