Alex
Reputation
304
Top tag
Next privilege 500 Rep.
Access review queues
 Sep24 awarded Autobiographer Dec25 awarded Yearling Sep18 awarded Commentator Sep18 awarded Editor Sep18 revised A polynomial has only real roots and all coefficients $\pm 1$. Prove the degree $<4$. added 5 characters in body; edited title Sep18 comment A polynomial has only real roots and all coefficients $\pm 1$. Prove the degree $<4$. Yes allow me to correct that. The source for the problem also made that mistake. Sep18 asked A polynomial has only real roots and all coefficients $\pm 1$. Prove the degree $<4$. Mar5 awarded Nice Question Mar1 awarded Teacher Mar1 answered Moving on the surface of a cube Mar1 comment Moving on the surface of a cube Excellent, because I posed this question to Brian randomly. My solution goes: $\frac{9!}{(3!)^{3}} - 3(2(\frac{6!}{(2!)^{2}}) + 6(\frac{5!}{(2!)^{2}}) + 6(\frac{4!}{2!}))$ Feb28 comment Moving on the surface of a cube What did you get Jorge? By the way, you can only use the 3rd 4th and 5th positions for the third letter. And, this can be done 3 times - for all the combinations of two letter. Feb28 awarded Critic Feb28 comment Moving on the surface of a cube I mean that they are travels where you must go on the inside of the cube, because the question asks for only surface or "outside" travels Feb28 comment Moving on the surface of a cube This is exactly my process and I counted 384 ways. 1680 including inside travels and 1296 on only inside travels. Someone can check Dec31 comment Proof of $\log_xy=\frac{\log_zy}{\log_zx}$ Also $\log_{z}x^\log_{x}y = \log_{z}y$ which you can then simplify to $y=y$ (And could someone edit this, because I am not understanding the programming) Dec27 awarded Nice Question Dec27 comment Prove that $\cot^2{(\pi/7)} + \cot^2{(2\pi/7)} + \cot^2{(3\pi/7)} = 5$ Interestingly enough, because of the symmetry of the roots, setting $x=\frac{1}{y^2}$ and using Vieta's formula on the $y^2$ term yields the same result. I assume that the other answer given also used Chebyshev polynomials of the first kind? I appreciate the explanation on the recursive nature of $cos(n\theta)$ Dec27 accepted Prove that $\cot^2{(\pi/7)} + \cot^2{(2\pi/7)} + \cot^2{(3\pi/7)} = 5$ Dec26 comment Prove that $\cot^2{(\pi/7)} + \cot^2{(2\pi/7)} + \cot^2{(3\pi/7)} = 5$ How is it known that $t^7−21t^5+35t^3−7t$ has roots $tan(r\pi/7)$