Results 1 to 5 of 5

Math Help - how can i prove this??plz help

  1. #1
    Newbie
    Joined
    Aug 2007
    Posts
    9

    how can i prove this??plz help

    If y = t^m + t^-m , x = t + t^-1, show that


    • (x^ 2 4) (dy/dx)^2 = m^2 (y^2 4)
    • (x^ 2 4) d^2y/dx^2 + x dy/dx (m^2)y = 0
    this is what i have done:-

    dy/dt = {(m)t^m-1} - {(m)t^-m-1}

    dx/dt = [(t^2)- 1]/ t^2

    then i calculated dy/dx

    dy/dx = [{(m)t^m+1} - {(m)t^-m+1}] / (t^2) -1}

    am i doing it right??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by slash View Post
    If y = t^m + t^-m , x = t + t^-1, show that
    • (x^ 2 4) (dy/dx)^2 = m^2 (y^2 4)
    You should find:

    <br />
\frac{dy}{dx}=m~\frac{t^m-t^{-m}}{t-t^{-1}}<br />

    so:

    <br />
\left[\frac{dy}{dx}\right]^2=m^2~\frac{(t^m-t^{-m})^2}{(t-t^{-1})^2}<br />
<br />
=m^2~\frac{t^{2m}+t^{-2m}-2}{t^2+t^{-2}-2}<br />
=m^2~\frac{y^2-4}{x^2-4}<br />

    rearrange and its done.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Slash, try to remember that "show that" and "prove" are not quite the same thing. Generally, "show that" is substantially simpler, often requiring only a little arithmetic. When it comes to "prove", that may be a new world. don't let "show that" scare you.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Jul 2007
    Posts
    90
    Quote Originally Posted by TKHunny View Post
    Slash, try to remember that "show that" and "prove" are not quite the same thing. Generally, "show that" is substantially simpler, often requiring only a little arithmetic. When it comes to "prove", that may be a new world. don't let "show that" scare you.
    But "prove that" should?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Thank you for making me clarify that. I thought better of it before submitting, but not better enough to change it. Let me add one qualification...

    If you INSIST on being scared by something, don't start with "show that". That's way too early. There is no NEED to be scared.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove a/b and a/c then a/ (3b-7c)
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 23rd 2010, 05:20 PM
  2. prove,,,
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 1st 2010, 09:02 AM
  3. Prove |w + z| <= |w| +|z|
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 28th 2010, 05:44 AM
  4. Replies: 2
    Last Post: August 28th 2009, 02:59 AM
  5. How to prove that n^2 + n + 2 is even??
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 30th 2008, 01:24 PM

Search Tags


/mathhelpforum @mathhelpforum