# Thread: how can i prove this??plz help

1. ## 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??

2. Originally Posted by slash
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:

$
\frac{dy}{dx}=m~\frac{t^m-t^{-m}}{t-t^{-1}}
$

so:

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

rearrange and its done.

RonL

3. 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.

4. Originally Posted by TKHunny
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?

5. 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.