Category: Algebra

Question Number 26582 by abdo imad last updated on 27/Dec/17 $$pisapolynomialhavingtheroots{x}_1,x_2,\dots x_n$$$$with{x}_i\ne x_{j}fori\ne jgivethedecomposition$$$$ofthefravtionF\left(x\right)=\frac{p^{{}^{\prime }}\left(x\right)}{p\left(x\right)}$$ Commented by abdo…

Question Number 92102 by  M±th+et+s last updated on 04/May/20 $$howcanwefactorize{x}^5-1?$$ Commented by mathmax by abdo last updated on 05/May/20 $${complex}\:{method}\:{z}^{\mathrm{5}} =\mathrm{1}\:\:\:{with}\:{z}\:={re}^{{i}\theta} \:\Rightarrow{r}^{\mathrm{5}}…

Question Number 92084 by Power last updated on 04/May/20 Answered by MJS last updated on 04/May/20 $$\mathrm{obviously}{x}_0=y_0=0$$$$\mathrm{let}x\ne 0\wedge y=px\wedge p\ne 0$$$$\begin{cases}{{x}\left(\left({p}^{\mathrm{5}} +\mathrm{1}\right){x}^{\mathrm{4}} −\mathrm{33}{p}\right)=\mathrm{0}}\{{x}\left(\mathrm{3}{p}^{\mathrm{2}}…

Question Number 157593 by metamorfose last updated on 25/Oct/21 $$letf:C\to R$$$$z\to min(y-\left[y\right],[y+1]-y),y=Im\left(z\right)$$$$letw=e^{i\frac{2\pi }{n}},n\in N^{\ast }$$$$evaluate{S}_n=\sum _{0⩽k<n}f\left(w^k\right)$$ Terms of Service…

Question Number 157585 by MathSh last updated on 24/Oct/21 $$\mathrm{if}0<\mathrm{a}⩽\mathrm{b}⩽\mathrm{c}<\frac{\pi }{2}\mathrm{then}:$$$$\frac{5}{\tan \mathbf{a}}+\frac{3}{\tan \mathbf{b}}+\frac{1}{\tan \mathbf{c}}⩾\frac{27}{\tan \mathbf{a}+\tan \mathbf{b}+\tan \mathbf{c}}$$ Answered by ghimisi last updated on 25/Oct/21 $$3(\frac{1}{tga}+\frac{1}{tgb}+\frac{1}{tgc})+2(\frac{1}{tga}-\frac{1}{tgc})⩾$$$$\mathrm{3}\centerdot\frac{\mathrm{9}}{{tga}+{tgb}+{tgc}}+\frac{\mathrm{2}\left({tgc}−{tga}\right)}{{tgatgc}}\geqslant\frac{\mathrm{27}}{{tga}+{tgb}+{tgc}} \…