From: u^2 = v^2 + (m/n)((u-v)^2) prove that : v/u = (m-n)/(m+n)

Expert Answers

An illustration of the letter 'A' in a speech bubbles

It is given that u^2 = v^2 + (m/n)((u-v)^2) and we have to prove that : v/u = (m-n)/(m+n)

u^2 = v^2 + (m/n)((u-v)^2)

=> u^2 - v^2 = (m/n)((u-v)^2)

=> (u^2 - v^2)/ (u-v)^2 = (m/n)

=> (u - v) ( u + v) / ( u - v)^2 = (m/n)

=> (u + v) / (u  - v) = m/n

=> (u + v) / (u  - v) + 1 = (m/n) + 1

=> (u + v + u - v) / (u - v) = (m + n) / n

=> 2u / ( u- v) = (m + n) / n

=> (u - v) / 2u = n/ ( m+ n)

=> (u - v) / u = 2n/ (m + n)

=> u / u - v / u = 2n / ( m + n)

=> 1 - v / u = 2n / ( m + n)

=> v / u = 1 - 2n / ( m + n)

=> v / u = (m + n - 2n ) / ( m+n)

=> v/ u = (m - n) / ( m + n)

We prove that v/u = (m - n)/( m + n) if u^2 = v^2 + (m/n)((u-v)^2)

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial