How to solve $\ln{x}+1−x^2=0$?
Studying the equation $\ln(x)- 1+ x^2=0$
let $a,b,c$ be postive real numbers ,and such $$ab+bc+ac=3$$   show that   $$\dfrac{a^2}{a+2b^2}+\dfrac{b^2}{b+2c^2}+\dfrac{c^2}{c+2a^2}\ge 1$$   This problem is from Secrets In Inequalities volume 1  page 30,example 1.24. the comment.the  author this case is a bit more diffcult,But this author can't post solution.Thank you How to interpret decomposition plot and check for seasonality How does vendor restocking work in Fallout 4? Storing hard crusted bread I'm currently baking a batch of sourdough bread. My last batch turned out perfectly with a hard crust and chewy inside. My problem is how to store the bread such that the crust stays hard. If I put it in a plastic bag the crust goes soft in a matter of hours and I'm afraid that the bread will turn dry if I leave it without some kind of protection. Note that I'm not looking for a long term storage solution.  What is the best way to store my bread, such that the crust stays hard and the inside stays chewy? Why didn't mastery of the Elder Wand move on from Harry? There's a lot of emphasis on Harry becoming the master of the Elder Wand after he defeats Draco. But what constitutes a “defeat”?  It seems that Harry wins a wrestling match with Draco, so now he’s the master of the Elder Wand.  But lots of other stuff happens to Harry: Nagini almost kills him, and he escapes just in time, but his wand breaks. The Snatchers chase him through the forest. He and his friends practically surrender (and Hermione even tries to disguise Harry). Voldemort almost kills Harry in the Forbidden Forest (or actually does, depending on how you look at it).  Why are none of these considered to be “defeats”? I'm new to modelbuilder and python. I have used modelbuilder to iterate through all rows in a shapefile (Points), process them, and produce a seperate output shapefile for each row.  The filename is generated using an inline variable (I think that is the correct terminology).  i.e. all output files have identical filenames except that the value of the PointID from the original input file is appended to the filename to enable them to be distinguished.  This works fine.  I've also written a python script to take the above output files from the model one at a time and do additional processing.  At present the input filename is hard coded into the script (i.e. I have to edit the script to change the input filename each time I run it).  Again this works fine while just processing a single file. However, I want to integrate the model and the python script so that I can run the script for each row in the original feature class automatically.  My question is therefore, how do I replace the hard coded name of the input file with a variable in the python script and how do I pass the filename to the script. A mod-only section of the help center Let $X$ be a topological space. The diagonal of $X \times X$ is the subset $$D = \{(x,x)\in X\times X\mid x \in X\}.$$   Show that $X$ is Hausdorff if and only if $D$ is closed in $X \times X$.   First, I tried to show that $X \times X \setminus D$ is open using the fact that $X \times X$ is Hausdorff (because $X$ is Hausdorff), but I couldn't find an open set that contains a point outside $D$ and is disjoint to it... Short story with aliens who hear their own thoughts as god-like voices I would have read this about 20-25 years ago.  I believe the subject was an alien individual, but it could have been a non-standard human instead.  The hook of the story was that the subject lacked an organ like the  that allows the halves of the brain to communicate efficiently, allowing the illusion of a single consciousness.  The subject is conscious, and has thoughts, but is subject to hearing commands like "Wash your hands!" "Fetch water!" within its head.  I recall the subject (and others like the subject) believing that the voices are their gods talking to them.  To the reader it becomes clear that this is a separate part of the subject's own mind that is responsible for long-term planning and simply can't communicate with the rest of the mind in the way a "normal" human is accustomed to. How to ignore certain files in Git File sync error (AUTH_FAILED) Recently I started getting a File sync error on all 3 of my PCs running Ubuntu One.  One is running Ubuntu, the other 2 are running Windows 8.  Looking at the list of clients on the web, none of them were there anymore.    I found this article:      On how to fix the issue for my Ubuntu PC and it worked perfectly.  Now I am looking for a similar fix for Windows but haven't found one yet.  I've tried un-installing Ubuntu One and re-installing it, but it must still be holding the keys somewhere because it never asked me to login again.    Does anyone know where I can clear these keys to get my files syncing on Windows again? How to install Tor? I tried to install Tor on my new version of Ubuntu, but it seems that Tor is not available in the repositories.  How else can I install and use Tor? Are counters (noun) physical things? Per the 's Wild Magic Surge table (PHB, p. 104)     07-08: You cast fireball as a 3rd-level spell centered on yourself.   There's other questionable area spells in that list (grease is a 10 foot square, so your square and which three?), but I'll focus on spheres like  (PHB p. 241):     (...) Each creature in a 20-foot-radius sphere centered on the point must (...)   My problem is, the sources I found so far - including the   to similar questions here - talk about measuring spheres from grid square intersections, whereas this clearly talks about it being centered on the unlucky Wild Magic sorcerer. Plus, since it's a wild magic effect, it doesn't exactly have a caster that can pick a point of origin. Is there an accepted way to measure an effect like this? SCJP6 regex issue How can I calculate sensor size (width and height) from focus length, vertical, and horizontal angle of view? I'm using Chrome 32 on an Android tablet (not phone) and just can't figure out how to close all open tabs in one go. Some Windows 10 UWP icons not displaying on search, or in settings How do I use the GUI to search for files in GNOME? On the command line I regularly use locate, or more often a locate x | grep y pattern to find a file I know exists but can't find!  I'd like something that did this quickly in the GUI. Can't find it if it's there.  Here's my confusion   In the applications/overview I can see Search and Indexing. This seems to be a configuration tool. But if this is a server, I can't find a client. In applications I find Nepomuk File Indexing -- I think this is a KDE thing? Ditto, no client? I've installed tracker. This is a strange mix of powerful and unreliable/limited. e.g. it doesn't find files like locate does (returns no results where locate returns 96 results), but is will unpack every tag I've added to my photos! And you can't limit by folder for a quick search within a folder. The old Gnome 2 Search for files... thing is not in the Accessories menu anymore.   I feel that this is basic/core-level functionality and I can't help feeling I'm missing something obvious. How to repeat a string a variable number of times in C++? I want to insert 'n' spaces (or any string) at the beginning of a string in C++. Is there any direct way to do this using either std::strings or char* strings?  E.g. in Python you could simply do  &gt;&gt;&gt; "." * 5 + "lolcat" '.....lolcat'