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In a very recent question the OP had made considerable amount of progress in proving an inequality. The OP was only left to prove the inequality $x^2y+y^2z+z^2x\le \frac{4}{27}$. Myself knowing that the inequality was quite famous (at least in the contest world). I voted to close it as duplicate of this one which helped the OP finish the proof. (And he/she acknowledges it.)

Thinking over it, I don't know whether what I did was correct. This post with which it has been associated as a duplicate is very different from the original question and it has particularly helped the OP. I really don't know whether I should have closed as a duplicate. Please advice

Should I have answered the question with the link? Or should I have just left it as a comment?

Also in general is it a practice in the site to close questions as a duplicate taking into account the OP's progress? (For example, in this case associating it with a post concerning a sub-inequality the OP was left to prove)

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    $\begingroup$ It looks like a good outcome to me. As the Question itself has a good bit of reasoning and is upvoted, it is likely to remain as a duplicate. In that way it will perhaps serve to direct interested Readers to the older Question for further information (obviating a duplication of efforts unnecessarily). $\endgroup$
    – hardmath
    Feb 3 at 4:19
  • $\begingroup$ I wonder why you have removed the tag related to duplicates when the question is clearly about closing as duplicates? $\endgroup$ Feb 3 at 11:04
  • $\begingroup$ @MartinSleziak I tried to bring in the tag duplicates but it seems the system is automatically changing it to 'exact duplicates ' which is not the case $\endgroup$ Feb 3 at 11:11
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    $\begingroup$ @MartinSleziak If my question was about 'exact duplicates' I should obviously close it,in this case they are not ,My confusion is what should I do if the post indirectly adresses the question as in this case.please help me to put the right tag $\endgroup$ Feb 3 at 11:14
  • $\begingroup$ @AlbusDumbledore I would suggest to continue the discussion related to the choice of tags in the tagging chatroom, so that we do not leave too many comments here. $\endgroup$ Feb 3 at 11:17
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    $\begingroup$ This post seems a bit related: Handling near duplicates. (Maybe also other posts linked there might be useful.) But it is definitely not the same. $\endgroup$ Feb 3 at 11:26
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It is definitely a judgement call - so various users might have various views on a specific question.

One issue is whether you consider this a question about the inequality $$\frac{x}{y^3+2xyz} + \frac{y}{z^3+2xyz} + \frac{z}{x^3+2xyz} \gt \frac{15}{2} \tag{1}$$ or whether you consider this a question whether about the inequality $$xy^2+yz^2+zx^2 < \frac{4}{27} \tag{2}.$$ (The OP writes that it suffices to prove $(2)$ to finish their approach)

If you consider this as a question about $(2)$, then it is an exact duplicate. If it is a question about $(1)$ then personally, I would consider a reasonable thing:

  • Posting an answer saying where solution for $(2)$ can be found. (Thus finishing the OP's approach.)
  • Leaving the question open, so that if somebody has entirely different approach to $(1)$, they still can post another answer.

In general, if we have question about some problem $(1)$ and we want to close it as a duplicate of a question about the problem $(2)$, we should have a look whether these two problems are close enough to each other. But I do not want to rehash here the previous discussions about this issue, I wrote about this at length here: How close a match we need to close a recurring question as a duplicate?

In this specific case, letting the question closed might be a reasonable outcome too.. Mainly because the OP agreed with the closure. (The fact that it is shown as closed by community means that this was chosen by the OP after the duplicate was suggested.) And if somebody wants to post a different approach as an answer, they can ask for the question to be reopened or simply post a new question.

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  • $\begingroup$ thanks for writing this up,one question: you mentioned an alternative of posting an answer saying where solution 2 can be found,I felt that was a good idea but are link only answers encouraged in this site? $\endgroup$ Feb 4 at 15:58
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    $\begingroup$ Yes, I am aware that the link answers are frowned upon. However, this is a bit special situation - since the OP says that they have already been able to get from $(1)$ to $(2)$ and they only need that to finish their approach. Here are some examples of my answers which consist mostly of links: $x^y = y^x$ for integers $x$ and $y$y](https://math.stackexchange.com/q/9505#78599), [Let $X$ be an infinite dimensional Banach space. Prove that every Hamel basis of $X$ is uncountable. (Although it is not the same situation as in this question.) $\endgroup$ Feb 4 at 16:12
  • $\begingroup$ Ok thanks I think if a similar case comes I shall answer with a link.Thanks for your input and the various links you have collected $\endgroup$ Feb 4 at 16:17
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    $\begingroup$ @Albus: When we say "link only answers" are discouraged, there is an emphasis on "only". Links are often used in Answers. When they are used the FAQ on how to write a good answer discusses providing context for links. The mention of external links there applies (perhaps to a lesser extent) to linking to previous Questions at Math.SE. $\endgroup$
    – hardmath
    Feb 5 at 15:25

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