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)<x(2-x) randomity, can you tell me why i cant do that way? |

zaphyBeeble | i think randomity's was better..always +ve |

Olathe | akSeya: If you multiply both sides by a negative, it changes the direction of the inequality. |

zaphyBeeble | and u get a cubic olathe if u do it randomity's way..hrmf... |

Olathe | Right. |

|Steve| | Is it so hard to figure out when (2-x)(x+3) is negative though? |

zaphyBeeble | so does it mean one more possibilty of x ? |