If A, B, C Are in Continued Proportion and A(B - C) = 2b, Prove that a - C = (2(A + B))/A - Mathematics

Sum

If a, b, c are in continued proportion and a(b - c) = 2b, prove that a - c = (2(a + b))/a

Solution

Since a, b, c are in continued proportion,

a/b = b/c

⇒ b2 = ac

∴ a(b - c) = 2b

⇒ ab - ac = 2b

⇒ ab - b2 = 2b

⇒ b(a - b) = 2b

⇒ a - b = 2

Now

L.H.S = a - c

= (a(a - c))/a

= (a^2 - ac)/a

= (a^2 -b^2)/a

= ((a - b)(a + b))/a

= (2(a + b))/a

= R.H.S.

Concept: Concept of Proportion
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