lone student

Well-known duplicate

I politely asked the moderator to delete my answer, because the question is just a dupe, not low quality. I didn't ask you to downvote me. The reason for downvoting an answer that will be deleted is purely and completely psychological. If I'm not mistaken, there's technically no point in downvoting an accepted answer to get it deleted.

@XanderHenderson Please delete this answer . Thanks.

@amWhy Hello $\ddot\smile$, how are you ?

Problematic answer and IMHO repeate essentially the above answer .

@MartinR It would be nice if you could share the results you got. It will be useful in the future.

Until the OP is active again, we need to give him/her reasonable time. If the OP doesn't make any edits to his/her answer after being active on the site again, then I think that, this answer should be deleted.

@ParamanandSingh Hello, I needed some guidance here. If possible, can you leave a comment on my answer to confirm whether my answer to this question is correct conceptually rather than algebraically? How consistent is my solution? Does the solution contain a trivial conceptual error? Thank you .

@robjohn Hello. How are you ? Do you have some time to help me? Can you check out a small solution in your area of ​​expertise?

@XanderHenderson Yes, exactly . That's how I ran it on my Android (5.1).

@s.harp Many Many thanks . This worked. I changed the language .

@s.harp Yes, exactly. Sorry please, I am aware here is not suitable for that question .

@s.harp Yes the problem is exactly language problem I couldn't catch how it happened.

@s.harp No. I controlled . Gboard works in English.

@s.harp Yes from my phone . I don't know how it happened.

@TedShifrin Can you help, how can I move into English for MathJax ?

@TedShifrin Hello . Can you show how can I fix the following issue ? My MathJax works in arabic. Many thanks.

@冥王Hades I had solved the 3rd and 4th degree polynomial equations in highschool, but then I found out that they were already solved. However, the method I use is not mentioned in Wikipedia. However, I still think someone else probably did.

@XanderHenderson Hello .

@TedShifrin I voted your answer. Thank you for your remarks .

@TedShifrin Yes, indeed .

@TedShifrin Thank you for your feedback. I thought in such way : Since $x=-y\iff y=-x$ and since if $ \frac{y}{x-z}=\frac{y+x}{z}=\frac{x}{y}$, then $y,z≠0$ otherwise the equality would not hold, therefore I thought that, I need only $x+y≠0$ for applying the Fraction Arithmetic . Therefore, I tried to show that, $x+y=0$ can not be possible, which contradicts with the problem statement. Therefore, the Fraction Arithmetic can be applied .

@TedShifrin I see, many thanks I appreciated .

@TedShifrin Interesting...Are the comments I left correct in this sense?

@TedShifrin Thank you. Not problem, I would gladly wait for you until you have a few seconds :-) .

@TedShifrin Would you like to leave a useful comment here I don't know, how can I eloborate .

@TedShifrin Hello.

@robjohn What I mean, in this answer, completing the square is "terminological" incorrect or "procedural" incorrect or "identity-like" incorrect ?Can you add further explanation, if possible...?

@robjohn It should be $$\begin{align}P(z):=\underbrace{\left(z^2+z+1\right)}_{\Delta_z<0}\left(z\color{red}{+}\frac {1}{z^2+z+1}\right)^2+\frac{\overbrace{3z^2+3z+2}^{\Delta_z<0}}{\underbrace{\color{black}{z}^2+{z}+1}_{\Delta_z<0}}\end{align}$$

Ahh, that was a not correct

@robjohn Thank you. Please, see the last comment, because I am going to delete the comment section after your first comment .

@robjohn Hello, good morning (in my location), If the comment section is inappropriate, please ping me as I should continue here.

@robjohn Wait aside with the votes. Do you see any wrong logic in that answer? The first answer seems not incorrect to me, but do you see a problem with the second answer? Hopefully, I'm not asking questions contrary to the purpose of the room. The important thing is not the downvote I get, I wouldn't want to be the person who gave a fake answer. Thank you.

@SoumikMukherjee Thank you .

@Jakobian Sure .

@robjohn Thank you for your replying . I mean, you got an unfair downvote too. I just wanted to point out. I was writing something like answers on the site with a broken and almost non-working phone. While I'm answering in the site, the owner of the small shop I work for always gets angry with me. I also feel bad psychologically when I get unfair downvotes while writing an answer with these conditions. Thank you.

Thank you very much, anyway @MartinSleziak

Hello @MartinSleziak . If you hava a little time, can you help me haw can I improve my answer ?

My question is: If we remove all Abel's and Ruffini's proofs from mathematics, what I mean is: If we remove all possible high school-level algebraic proofs from mathematics about the solution of the 5-degree general quintic, then does Galois theory or Galois's new conception prove that the 5-degree general quintic has no general solution alone ? Or, does the Galois theory work after proving algebraic insolvability? (+1)

@lulu On this point $35=7^15^13^02^0$, then $35=1100$ ?

@wjmccann $1=2^0$ is not a prime. But you wrote $15=5^13^1\color{red}{2^0}$. I didn't get this point, why is not $15=11$ ?

@lulu Because, otherwise $12=3^1\cdot 2^2\cdot 5^0$, then $12=120$

@lulu To me, it should be $15=11$, otherwise we have ,e.g. $15=1100$ which seems not reasonable to me.

@TheAmplitwist Many thanks for your suggestion !

@TheAmplitwist Yes, exactly

@TheAmplitwist Thank you. Almost close to my code . But, I want only the same color parts be aligned

@MartinSleziak Thank you very much for your helpful comments!

Yes. I agree. I will use this suggestion which seems nice to me.