SOLUTION: if a,b,c,d are in continued proportion, prove that (a+b)(b+c)-(a+c)(b+d)=(b-c)^2

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Question 519299: if a,b,c,d are in continued proportion, prove that (a+b)(b+c)-(a+c)(b+d)=(b-c)^2
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
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)²
(3+9)(9+27)-(3+27)(9+81)≟(9-27)²
       (12)(36)-(30)(90)≟(-18)²
            432 - 2700  ≟ 324
                 -2268  ≠ 324
 
Edwin
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