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Algebra with a complicated function

  • Thread starter Nusc
  • Start date
  • #1
753
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Homework Statement



[tex]
\frac{\pi(1+2\alpha)}{t}=x \&\& ((\alpha \geq 0 \&\& 1+ 2\alpha < 4\beta \&\& \pi \sqrt{-(1+2\alpha)^2+16\beta}=2t)\\ ||((1+2\alpha>0 \&\& 2\alpha < 1 +4 \beta \&\& \beta \geq 0 \&\& \pi \sqrt{(-1+2\alpha -4\beta) (3+2 \alpha +4\beta)}=2t)
[/tex]

[tex]
\alpha and \beta[/tex]are integers.

This is a solution I obtained from Mathematica, it's ugly as you can tell. How can I generalize this concisely?
How can I find a general expression for x from this equation?

Homework Equations





The Attempt at a Solution



If we look at the first condition, [tex] \alpha \geq 0 [/tex] which is nice
\alpha \beta 1+2*alpha < 4*beta
0 1 1 < 4
1 2 3 < 8
2 3 5 < 12


This is false when
\alpha \beta 1+2*alpha < 4*beta
0 0 1 < FALSE
1 1 3 < 4
2 2 5 < 8

Any suggestions?
 
Last edited by a moderator:

Answers and Replies

  • #2
753
2
Based on the equality for condition 1, we also know that [tex]\beta >0[/tex] but how do you generalize the order?

Can this even be generalized to start with? I think not, but how can you tell? There are two condition I have to take into account.
 

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