Question

If a, b, c are in continued proportion, then prove that b/b+c=a-b/a-c

Answer 1

Answer:

b/b+c=a-b/a-c

Step-by-step explanation:

a, b, c are in continued proportion

=> a/b = b/c = K

=> a = bK   & b = cK

=> a = CK²

To be Proved that

b/(b + c) =  (a - b)/(a - c)

LHS =

b/(b + c)

= cK/(cK + c)

= K/(K + 1)

RHS

(a - b)/(a - c)

= (cK² - cK) /(cK² - c)

= K(K - 1) /( K² - 1)

= K (K - 1) / ( (K + 1)(K - 1) )

= K /(K + 1)

LHS = RHS

b/b+c=a-b/a-c

Answer 2

$\huge\underline\mathfrak\green{Solution}$