(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[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?

2. Relevant equations

3. 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Algebra with a complicated function

**Physics Forums | Science Articles, Homework Help, Discussion**