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Category: Algebra

let-p-x-x-10-1-1-find-roots-of-p-x-2-factorize-i-nside-C-x-p-x-3-factorize-inside-R-x-p-x-

Question Number 42195 by math khazana by abdo last updated on 20/Aug/18 $${let}\:{p}\left({x}\right)={x}^{\mathrm{10}} −\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{i}\:{nside}\:\:{C}\left[{x}\right]\:{p}\left({x}\left\{\right.\right. \\ $$$$\left.\mathrm{3}\right)\:{factorize}\:{inside}\:{R}\left[{x}\right]\:{p}\left({x}\right)\:. \\ $$ Answered by maxmathsup…

Solve-for-real-numbers-0-x-t-2-t-sinh-t-cosh-t-2-dt-0-

Question Number 173250 by Shrinava last updated on 08/Jul/22 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\int_{\mathrm{0}} ^{\:\boldsymbol{\mathrm{x}}} \:\frac{\mathrm{t}^{\mathrm{2}} }{\left(\mathrm{t}\:\centerdot\:\mathrm{sinh}\:\mathrm{t}\:−\:\mathrm{cosh}\:\mathrm{t}\right)^{\mathrm{2}} }\:\mathrm{dt}\:=\:\mathrm{0} \\ $$ Answered by Ar Brandon last updated on…

Question-173228

Question Number 173228 by mathlove last updated on 08/Jul/22 Answered by Frix last updated on 08/Jul/22 $$\mathrm{let}\:\mathrm{sin}\:\frac{\pi}{\mathrm{11}}\:={s}\:\wedge\:\mathrm{cos}\:\frac{\pi}{\mathrm{11}}\:={c} \\ $$$$\left(\mathrm{1}\right)\:\Rightarrow\:{y}={s}^{\mathrm{2}} {x}−\frac{{s}^{\mathrm{4}} }{\mathrm{4}} \\ $$$$\left(\mathrm{2}\right)\:\Rightarrow\:{y}=\frac{{x}}{{c}^{\mathrm{2}} }+\frac{{c}^{\mathrm{2}} }{\mathrm{4}}…