## #math - Sun 22 Apr 2007 between 19:36 and 19:49

### NY Lost Funds

 linolium is the negative zero of 2^x = x^2 irrational? zaphyBeeble x=2 Manyfold i always thought 0 has no sign powerfox |Steve|: Thanks! |Steve| np linolium maybe I'm using the wrong term here.. but I get x = 2, 4, and -0.766665 zaphyBeeble yep x=4 |Steve| There appear to be 2 negative solutions that mathematica can find.They are definitely not rational. linolium two?! zaphyBeeble how does it solve it? |Steve| But they might be the same. I can't tell.Oh, one of them turned out to be 4. zaphyBeeble x log 2 = 2 log x => log 2 /2 = log x / x |Steve| (-2*ProductLog[-1, -Log[2]/2])/Log[2] is what it found% Simplify[ (-2*ProductLog[-1, -Log[2]/2])/Log[2]] mbot |Steve|: (-2*ProductLog[-1, -Log[2]/2])/Log[2] |Steve| % FullSimplify[ (-2*ProductLog[-1, -Log[2]/2])/Log[2]] mbot |Steve|: 4 linolium what does ProductLog do? |Steve| No idea. Olathe % ProductLog::usage mbot Olathe: "ProductLog[z] gives the principal solution for w in z = w e^w. ProductLog[k, z] gives the kth solution." akSeya hi there...how to solve this inequation: ((x+1)/(2-x))<(x/(3+x)) powerfox |Steve|: I don't know what to do next :( |Steve| powerfox: Partial fraction decomposition. RadSurfer If I wanted to find a pdf theory on how triple integrals work, and what they are applied too, could someone help me? randomity akSeya: multiply both sides by (2-x)^2*(3+x)^2 ? |Steve| pdf being probability density function? powerfox |Steve|: ok, thanks. I will try Olathe akSeya: Multiply both sides by 2-x. You should get two answers: one if 2-x is positive, one if it's negative. akSeya randomity, i tried to multiply (x+1)(3+x)