From: u^2 = v^2 + (m/n)((u-v)^2) prove that : v/u = (m-n)/(m+n)
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
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)
Related Questions
- Prove that u + v = v + u for any u and v in R^n.
- 1 Educator Answer
- Prove 1(1!) + 2(2!)+3(3!)+...+n(n!)=(n+1)!-1 by using mathematical induction
- 1 Educator Answer
- Use mathematical induction to prove that 2+4+6+...+2n = n^2+n true for all natural numbers
- 1 Educator Answer
- Prove the following reduction formula: integrate of (tan^(n)x) dx= (tan^(n-1)x)/(n-1) - integrate...
- 2 Educator Answers
- Determine values of m&n such that vector v(m-2, m+n, -2m+n) & w(2,4,-6) have same direction.
- 2 Educator Answers
We'll subtract v^2 both sides:
u^2 - v^2 = (u-v)(u+v)
We'll write (u-v)^2 = (u-v)(u-v)
We'll re-write the given expression:
(u-v)(u+v) = m(u-v)(u-v)/n
We'll simplify both sides:
u+v = m(u-v)/n
We'll multiply by n:
nu + nv = mu - mv
We'll move the terms in u to the left side and the terms in v to the right side:
nu - mu = -mv - nv
u(n-m) = -v(m+n)
u(m-n) = v(m + n)
We'll divide by u:
v(m + n)/u = m-n
We'll divide by m+n:
v/u = (m-n)/(m+n) q.e.d.
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Student Answers