Category: Algebra

Question Number 19435 by Tinkutara last updated on 11/Aug/17 $$\mathrm{If}\alpha =\cos \frac{2\pi }{5}+i\sin \frac{2\pi }{5},\mathrm{then}\mathrm{find}\mathrm{the}$$$$\mathrm{value}\mathrm{of}\alpha +{\alpha }^2+{\alpha }^3+{\alpha }^4.$$ Answered by ajfour last updated on 11/Aug/17 $$\underset{\mathrm{r}=\mathrm{1}}…

Question Number 150489 by mathdanisur last updated on 12/Aug/21 $$\underset{0}{\stackrel{2}{\int }}\mid \mathrm{x}\mid {\mathrm{x}}^{[\mathbf{x}+1]}\mathrm{sgn}\left(\mathrm{x}\right)\mathrm{dx}=?$$ Answered by Olaf_Thorendsen last updated on 12/Aug/21 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{2}} \mid{x}\mid.{x}^{\left[{x}+\mathrm{1}\right]}…

Question Number 150486 by mathdanisur last updated on 12/Aug/21 $$\mathbf{x}\in \mathbb{R}$$$$\mid \mathrm{x}-1\mid +\mid \mathrm{x}+3\mid +\mid \mathrm{x}-5\mid$$$$\mathrm{find}\mathrm{the}\mathrm{smallest}\mathrm{value}\mathrm{of}\mathrm{a}\mathrm{given}$$$$\mathrm{expression}$$ Commented by MJS_new last updated on 12/Aug/21…

Question Number 19403 by Tinkutara last updated on 10/Aug/17 $$\mathrm{Let}P\left(n\right)=(n+1)(n+3)(n+5)(n+7)(n+9).$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{largest}\mathrm{integer}\mathrm{that}\mathrm{is}\mathrm{a}$$$$\mathrm{divisor}\mathrm{of}P\left(n\right)\mathrm{for}\mathrm{all}\mathrm{positive}\mathrm{even}$$$$\mathrm{integers}n?$$ Commented by RasheedSindhi last updated on 12/Aug/17…

Question Number 19405 by $@ty@mlastupdatedon10/Aug/17$$Converti\sqrt{\frac{2\sqrt{2}-1}{2}}intopolarform.$$AnsweredbyTinkutaralastupdatedon10/Aug/17$$\sqrt{\frac{2\sqrt{2}-1}{2}}(\cos \frac{\pi }{2}+i\sin \frac{\pi }{2})$$Commentedby$@ty@m…