#### Question

If a, b and c are in continued proportion, prove that: a: c = (a^{2} + b^{2}) : (b^{2} + c^{2})

#### Solution

Given a, b and c are in continued proportion

=> a : b = b : c

Let `a/b = b/c = k` (say)

=> a = bk, b = ck

Now L.HS = `a/c = ck^2/c = k^2`

R.HS = `(a^2 + b^2)/(b^2 + c^2)`

`= ((ck^2)^2 + (ck)^2)/((ck)^2 + c^2)`

`= (c^2k^2(k^2 + 1))/(c^2(k^2 + 1))`

`= k^2`

LHS = RHS

Is there an error in this question or solution?

Solution If A, B and C Are in Continued Proportion, Prove That: A: C = (A2 + B2) : (B2 + C2) Concept: Proportions.