Category: Algebra

Question Number 49186 by afachri last updated on 04/Dec/18 $$\mathbf{please}\mathbf{help}\dots$$$$$$$$\mathrm{There}\mathrm{is}:$$$$21{\mathit{x}}^2-21\mathit{p}\mathit{x}+49\mathit{p}-7=0$$$$\mathrm{whose}\mathrm{roots}\mathit{u}\mathrm{and}\mathit{v}.\mathrm{If}\mathit{u}\mathrm{and}\mathit{v}\mathrm{are}\mathrm{not}\in \mathbb{Z},$$$$\mathrm{and}\mathit{u},\mathit{v}⩾1.$$$$\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\mathit{u}+\mathit{v}!$$$$…

Question Number 49177 by rahul 19 last updated on 04/Dec/18 $$If\mid z_1-z_2\mid =\mid z_1\mid +\mid z_2\mid ,thenprove$$$$thatarg\left(\frac{z_1}{z_2}\right)=\pi .$$ Answered by MJS last…

Question Number 180236 by mnjuly1970 last updated on 09/Nov/22 $$\mathrm{calculation}$$$$\mathrm{\Omega }=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{\zeta \left(2n\right)}{4^n}\stackrel{?}{=}\frac{1}{2}$$$$\:\Omega\:=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left\{\frac{\mathrm{1}}{\mathrm{2}^{\:\mathrm{2}{n}} }\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{k}^{\:\mathrm{2}{n}} }\:\right\} \…

Question Number 49151 by rahul 19 last updated on 03/Dec/18 $$Letziscomplexnumbersatisfying$$$$theequation{z}^2-(3+i)z+m+2i=0,$$$$wheremϵR.Supposetheequation$$$$hasarealroot,thenfindthenonrealroot?$$ Answered by mr W last…

Question Number 180211 by Shrinava last updated on 09/Nov/22 $$\mathrm{Find}:$$$$\mathrm{\Omega }=\gcd (4^{2020}-1,8^{2021}-1).\mathrm{Generalization}.$$ Answered by puissant last updated on 09/Nov/22 $$\Omega\:=\:{gcd}\left(\mathrm{2}^{\mathrm{4040}} −\mathrm{1}\:;\:\mathrm{2}^{\mathrm{6063}}…