I am stuck trying to find the minimum polynomial of $\sqrt[3]{9} + \sqrt[3]{3} - 1$ over $\mathbb{Q}$. I have tried using  method and  method but none of them seem to be working in this case. Can anyone give me a hint?
Find the minimal polynomial for $\sqrt[3]{2} + \sqrt[3]{4}$ over $\mathbb{Q}$  I havent covered galois theory, this is an exercise from the chapter algebraic extensions in gallian.  I can see that $\sqrt[3]{2} + \sqrt[3]{4}$ $\in \mathbb{Q}(2^{1/3})$, after this I am clueless.  Need hints will finish the proof.
If I use  two different router in the same network while both are running in the default router mode then we can access the setup page or setup interface from browser just by IP address of corresponding router. But when I use one of the router as repeater then I can only enter the setup page of the router which is running in router mode. Why router's setup page cannot be accessed when using the router as repeater? Now how can I change the settings of the router in repeater mode? The only way is to reset router with the hardware key then setup again. Proving $\frac{x}{y} +\frac{y}{z} + \frac{z}{x} \ge 3$ for positive $x,y,z$ Suppose $x,y,z$ are real positive numbers, prove that: $$\dfrac{x}{y} +\dfrac{y}{z} + \dfrac{z}{x} \ge 3$$ with equality when $x=y=z$.  Can someone help me find an easier solution? I started with assume only two are equal, without loss of generality, $x=y$. Then we get $$1 + \dfrac{x}{z} + \dfrac{z}{x}$$ $$1 + \dfrac{x^2 + z^2}{xz} = 1+ \dfrac{(x-z)^2 + 2xz}{xz} = 1 + 2 + \dfrac{(x-z)^2}{xz} \ge 3$$ To prove the general result I considered using a derivative with respect to $y$ to show that, starting with $x=y$ and increasing $y$ by a tiny amount, will show the equation's derivative as positive. I haven't gotten this to work yet. Any ideas? I have a module with a page callback handler for the path "products". So if the user navigates to products/apples then the module presents a page about our apples, and if they go to products/oranges then etc. These pages include detail about the various products.  I would like XML Sitemap to be populated from my module. After all, it's my module that knows what products exist, their descriptions etc.  Any hook or anything I can use for that? I'd like to manage my home machines and laptops with Landscape, how can I do this? How can Star Trek: Countdown ever be considered canon? What do bookcases do for enchanting? Calculating the longest distance within polygon in QGIS I want to calculate the "diameter" of polygons in QGIS.  The "diameter" defined as the distance between the two most distant points of the polygon.  I couldn't find a fitting solution in the field calculator. Maybe you have some ideas? Printing pointers in C Passport validity for Canada I am traveling from Boston to Canada by cruise ship. The first port of arrival is on July 30 and the last port in Canada is on August 4. Then I'm flying on August 5 from Montreal to California. My passport is valid until August 20th. Will I have a problem? I 'had' better get going (Why 'had'??) Is it possible to create a counter just with wiring? With the new logic gates in the 1.3.1 update, is it possible to create some wiring circuit that counts how many times a trigger was activated? In other words, is it possible to make a circuit that outputs a trigger every two input triggers?  I've done some experimenting but the nature of wires and there being no intrinsic on/off state in Terraria makes it pretty counter-intuitive compared to real world logic circuits. Is it OK for OSB3 boards to get wet during construction? Why are we in love "with" someone? Square and square root and negative numbers Are they equal?      -5 = $\sqrt{(-5)^2}$ Probability of a painted cube being reassembled into itself Suppose 27 cubes are stacked together, suspended in the air, to form a larger cube.  The cube is then painted on all the exposed surfaces and dried.  The smaller cubes are then randomly permuted in both spatial position and spatial orientation to form another large cube.  What is the probability that new larger cube is identical to the original?  This is not homework, it was passed on by a friend who found it somewhere on the internet, and they do not remember where. Driver locked memory on a non-virtual machine I am trying to install  under Wine. The program setup continually requests proxy settings. My broker tells me this shouldn't happen, and is a problem on my end. Here is what I have tried to attempt to solve this error:   I have gone into Network settings and proxy is set to none. I have looked in Wine Regedit and proxy_enable is set to 0. I have checked the firewall settings on my modem. I have tried reinstalling wine. I have installed lib32nss-mdns I can log on to my modem in iexplore using the gateway ip but thats it I've set my DNS to 10.0.0.138 to reflect the gateway I've set up a 32 bit Wine prefix   How should I proceed in solving this? Welcome back message suggests to upvote questions and answers even when questions are locked I just opened a URL to a question on programmers.SE and got the message:     But the question was locked, so I couldn't do what it asked me to do.  I consider this to be a very minor edge case bug and it's likely not worth investing developer time into it. But since this  I guess it's worth reporting even if it's just for making you aware of it. I'm giving Deus Ex a quick playthrough as a refresher before jumping into Human Revolution. In the interest of expediency, I've decided to cheat. ^.^  Normally, cheats must be re-enabled for each level when playing the original DX. I've encountered instructions on several sites (word-for-word identical instructions, so clearly copy/pasted) for permanently enabling cheats, but they aren't working for me:     Because you will need to redo this for every level, you can open up 'user.ini' and add 'bCheatsEnabled True' in the [DeusEx.DeusExGameInfo] section of the file to allow cheats to be activated forever.   Not only is that not working for me, it doesn't even look right compared to the rest of the file (space instead of =). With increasing desperation, I've tried adding that line (both verbatim and switching to an equal sign) to every section of both User.ini and DeusEx.ini which looks even remotely plausible — even creating a [DeusEx.JCDentonMale] section, just in case.  Does anyone know how to get this working? I'm running DX:GOTY version 1.112fm from Steam on Windows 7. What is the purpose of Microsoft.SharePoint.Runtime.dll in CSOM? I know we need to use Microsoft.SharePoint.Client and Microsoft.SharePoint.Client.Runtime dll's reference in .NET managed CSOM application development. But can someone help me understand why we have to use Microsoft.SharePoint.Client.Runtime and whats it's purpose, in detail. or point me to a reference please. Thank you in advance