Question

If a,b,c and d are in continued proportion, show that (a-b):(a+b)=(a-d):(a+2b+2c+d)​

Answer 1

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