ICSE Class 10CISCE
Share
Notifications

View all notifications

If A, B, C Are in Continued Proportion, Prove That (A + B + C) (A – B + C) = A2 + B2 + C2 - ICSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

Question

If a, b, c are in continued proportion, prove that (a + b + c) (a – b + c) = a2 + b2 + c2

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

  Is there an error in this question or solution?

APPEARS IN

 2014-2015 (March) (with solutions)
Question 6.1 | 3.00 marks
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.
S
View in app×