Category: Algebra

Question Number 151905 by mathdanisur last updated on 24/Aug/21 Answered by mindispower last updated on 24/Aug/21 $$\mathrm{8}{x}^{{x}} {y}^{{y}} {z}^{{z}} \mathrm{2}^{{x}+{y}+{z}} =\mathrm{2}\left(\mathrm{2}{x}\right)^{{x}} .\mathrm{2}\left(\mathrm{2}{y}\right)^{{y}} .\left(\mathrm{2}{z}\right)^{{z}_{} } \…

Question Number 151889 by mathdanisur last updated on 23/Aug/21 $$\mathrm{Compare}:$$$$\sqrt[2020]{{(2020!)}^3}\mathrm{and}505\cdot {2021}^2$$ Answered by MJS_new last updated on 24/Aug/21 $$\forall{n}\in\mathbb{N}\mid{n}>\mathrm{1}:\left({n}!\right)^{\frac{\mathrm{3}}{{n}}} <\frac{{n}}{\mathrm{4}}×\left({n}+\mathrm{1}\right)^{\mathrm{2}} \…

Question Number 151884 by mathdanisur last updated on 23/Aug/21 $$\mathrm{f}\left(\mathrm{x}\right)=(\mathrm{x}-1)(\mathrm{x}-2)\dots (\mathrm{x}-2021)$$$$\mathrm{f}{}^{{}^{\prime }}\left(2021\right)=?$$ Answered by mr W last updated on 24/Aug/21 $$\mathrm{ln}\:{y}=\mathrm{ln}\:\left({x}−\mathrm{1}\right)+\mathrm{ln}\:\left({x}−\mathrm{2}\right)+…+\mathrm{ln}\:\left({x}−\mathrm{2021}\right) \…

Question Number 20800 by Tinkutara last updated on 03/Sep/17 $$\mathrm{If}\mathrm{Re}\left(\frac{z+4}{2z-1}\right)=\frac{1}{2},\mathrm{then}z\mathrm{is}\mathrm{represented}$$$$\mathrm{by}\mathrm{a}\mathrm{point}\mathrm{lying}\mathrm{on}$$$$\left(1\right)\mathrm{A}\mathrm{circle}$$$$\left(2\right)\mathrm{An}\mathrm{ellipse}$$$$\left(3\right)\mathrm{A}\mathrm{straight}\mathrm{line}$$$$\left(4\right)\mathrm{No}\mathrm{real}\mathrm{locus}$$ Commented by ajfour…

Question Number 151849 by mathdanisur last updated on 23/Aug/21 Commented by Rasheed.Sindhi last updated on 23/Aug/21 $$Specialgeneralcase$$$$x=y=z(primeof4m+3type)$$$$\frac{{z}^{\mathrm{2}{k}} +{z}^{\mathrm{2}{k}} }{{z}^{{k}} +{z}^{{k}} }=\frac{\mathrm{2}{z}^{\mathrm{2}{k}}…