If a, b,c,d are in continued proportion prove that

(a-b)^3 / (b-c)^3= a/d

 

Asked by arorasweety557 | 20th May, 2020, 02:16: PM

Expert Answer:

a, b, c, d are in continued proportion
Therefore, we have
a/b = b/c = c/d = k (say)
c=dk, b=ck=dk2, a=bk=dk3
Consider,
(a-b): (b-c)3
= (dk3 - dk2)3 : (dk2 - dk)3 
= d3k6(k - 1) : d3k3(k - 1)
= k3
 
a/d = dk3/d = k3
 
Hence, (a-b): (b-c)3 = a : d

Answered by Renu Varma | 20th May, 2020, 07:13: PM