Note: This is only an example question. An equivalent question already exists on the main site. I have posted the question here (but immediately deleted it) just to see what will be shown in the list of related questions. The post is still visible to users who have privilege to view deleted questions.
Search before asking
It is good to search before asking. It is possible that somebody asked about a similar problem in the past. You can use either built-in search or use your favorite search engine and restrict searching to this site. There are also some tools designed specifically for searching mathematical expressions. Various tips on searching on this site can be found, for example, here.
Admittedly, searching for questions on this site might be quite difficult. Searching for mathematical formulas is especially problematic. But the SE software helps you in finding similar questions during the process of writing the question. So we will get back to this.
It is good to choose the title which describes the topic of your question as well as possible.
- Bad: How to prove this inequality?
- Good: How to prove that $x^2+y^2\ge 2xy$?
Search for similar titles
Notice that after you wrote the title for your question, SE software lists questions with similar title above edit box (under the caption "Questions that may already have your answer".)
At this point, you might check whether some of the questions displayed there answers your question. If you found such question, or even several of them, you can read the answers given there. (Of course, if you have problems understanding other answers, it is still ok to ask about explanation. But in such case, you should clearly state what part of the answer you have problems with and you should link to the posts you have already read.)
Add the context to the question
Good question should contain context. In particular, you should include where you encountered the question. And you should also explain what have you tried so far. Do not forget to include all necessary details.
Bad: How can I show that $x^2$+$y^2$ $\ge$ $2xy$?
Note that in the above example, the question does not contain all necessary details. (Are you interested in this inequality for integers? Or for positive real numbers? For any real numbers?) No attempts to solve the problem are shown. And we also do not learn where does the question come from or why your are interested in.
Better: How can I show that $x^2$+$y^2$ $\ge$ $2xy$ for any real numbers $x$, $y$?
I have seen this inequality used in another post on this site, but I do not know how to prove it.
I can see that that this is true if $xy<0$, since both $x^2\ge0$ and $y^2\ge0$.
I tried to change the right hand side to $2xy=xy+xy$. But this did not help too much, since I cannot have both $x^2\ge xy$ and $y^2\ge xy$.
Try to choose correct tags
Before posting the question, you also have to choose tags. (This might be tricky for new users, but eventually you will learn which tags are used.) But also if you do not have much experience with the tag system, the SE system tries to help you. As you start typing in the tag field, you can see all tags containing the string you typed together with their tag-excerpts. Reading the tag-excerpts might help you decide whether the tags are appropriate for your question.
For example, if I have the question described above, I might try to describe what questions contains. There is an inequality. When I start typing this word, I see that the tag inequality indeed exists. I might decide to try to post that the inequality contains squares $x^2$ and $y^2$. So if I type the word square, I see that the tags square-numbers and sum-of-squares exist. However, if I read the displayed tag-excerpts, I see that they are for questions about squares of integers. So they are not suitable for my question.
See also: How am I supposed to use tags?
Look at similar and related questions
Notice that after you filled the body of the question and the tags, the list of similar question on the right is created by SE software. Again you should look among these questions to see whether your question has not been asked before.
And also after you post, list of related questions is shown in the side-bar on the right. You should check those questions, too.
Both similar and related questions are suggested based on tags, title, and various keywords appearing in your post.
Learn from improvements of your question
Other users might edit your question. Maybe they will leave you an explanation of the edit in a comment in the edit summary. But even if they don't, you might learn from their edits. For example:
- Somebody might add algebra-precalculus tag to your question. So you learn about existence of this tag and you might read the tag-info to see what questions this tag is suitable for.
- Somebody might change
$x^2$+$y^2$ $\ge$ $2xy$ to
$x^2+y^2 \ge 2xy$. You will learn from this edit that you do not have to enter each part of a mathematical formula separately, but you can enter the whole formula as one expression.
Learn from comments to your question
After you post a question, you might receive comment from other users. For example, user called Bob might post a comment like this: "Hint: Try to expand $(x-y)^2$." If you can solve the problem yourself using the hint, then you should try to post this as an answer to your question. (Unless an answer based on the same approach has already been posted.) If you have problems to solve the question using the hint, you can try to ask the user posting the hint what they mean. In such case it is good to ping the user, i.e., start your comment by @username, so that the user is notified. For example: "@Bob I get $(x-y)^2=x^2-2xy+y^2$. But I still do not see how this helps me to prove the inequality. Can you elaborate, please?"