Question 519299
if a,b,c,d are in continued proportion, prove that 

(a+b)(b+c)-(a+c)(b+d)=(b-c)^2.
<pre>
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)&#8799;(b-c)²
(3+9)(9+27)-(3+27)(9+81)&#8799;(9-27)²
       (12)(36)-(30)(90)&#8799;(-18)²
            432 - 2700  &#8799; 324
                 -2268  &#8800; 324
 
Edwin</pre>