1. ## How to start?

Hi

I have been scratching my head over this problem.

Find s,t,u and v if s^2 + t^2 + u^2 + v^2 - st - tu -uv - v + 2/5 = 0

gentsl

2. Originally Posted by gentsl
Hi

I have been scratching my head over this problem.

Find s,t,u and v if s^2 + t^2 + u^2 + v^2 - st - tu -uv - v + 2/5 = 0

gentsl
Are s, t, u, and v integers or real numbers?

-Dan

3. Originally Posted by gentsl
Hi

I have been scratching my head over this problem.

Find s,t,u and v if s^2 + t^2 + u^2 + v^2 - st - tu -uv - v + 2/5 = 0

gentsl
I too have been scratching my head over this problem.
Are you using parenthesis correctly?
It mostly looks like a candidate for the following manipulations:

$2s^2 + 2t^2 + 2u^2 + 2v^2 - 2st - 2tu -2uv - 2v + \frac45 = 0$
$s^2 + (s-t)^2 + (t-u)^2 + (u-v)^2 + (v - 1)^2 - \frac15 = 0$

Are s, t, u, and v integers or real numbers
How can integer solutions exist if the last thing is a fraction?

4. Originally Posted by Isomorphism
How can integer solutions exist if the last thing is a fraction?
(Ahem!)

-Dan

5. It is not stated if they are integers or real numbers.

Thanks Isomorphism for pointing that out. Just curious, if any of you went all the way to get s,t,u and v.

By the way, I wasn't notified by email of replies to this thread. I wonder why.

gentsl

6. Originally Posted by gentsl
It is not stated if they are integers or real numbers.

Thanks Isomorphism for pointing that out. Just curious, if any of you went all the way to get s,t,u and v.

By the way, I wasn't notified by email of replies to this thread. I wonder why.

gentsl
Isomorphism has done most of the hard work ...... Perhaps the following will keep the ball rolling for you:

Originally Posted by Isomorphism
$s^2 + (s-t)^2 + (t-u)^2 + (u-v)^2 + (v - 1)^2 - \frac15 = 0$
$\therefore s^2 + (s-t)^2 + (t-u)^2 + (u-v)^2 + (v - 1)^2 = \frac{1}{5}$

So obviously (why?) each term on the left hand side has to be less than 1/5. This leads to a system of simultaneous inequalities ......

7. Originally Posted by gentsl
By the way, I wasn't notified by email of replies to this thread. I wonder why.
that's strange. check your user control panel. go to "edit options" and ensure that all the relevant checks and settings are set in the message and notification section.

otherwise, check to make sure you are subscribed to this thread (you should be automatically since you created it, but you never know...). click on "thread tools" and if you see "subscribe to this thread" in the drop down menu, click it

if all that doesn't work, send a PM to one of the administrators