#### Question

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

#### Solution

Given that a, b and c are in continued proportion

`=> a/b = b/c => b^2 = ac`

L.H.S = (a + b + c)(a - b + c)

= a(a - b + c) + b(a - b + c) + c(a - b + c)

`= a^2 - ab + ac + ab - b^2 + bc + ac - bc + c^2`

`= a^2 + ac - b^2 + ac + c^2`

`= a^2 + b^2 - b^2 + b^2 + c^2` [∵ `b^2 = ac`]

`= a^2 + b^2 + c^2``

=R.H.S

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#### APPEARS IN

Solution If A, B, C Are in Continued Proportion, Prove That (A + B + C) (A – B + C) = A2 + B2 + C2 Concept: Compound Interest as a Repeated Simple Interest Computation with a Growing Principal.