Category: Algebra

Question Number 192839 by Mingma last updated on 29/May/23 Answered by witcher3 last updated on 02/Jun/23 $$\mathrm{we}\mathrm{see}\mathrm{that}2,7{\mathrm{can}}^{\prime }\mathrm{t}\mathrm{bee}\mathrm{factor}\mathrm{of}\mathrm{n}$$$$\mathrm{and}11\mid \mathrm{n}$$$$\mathrm{if}\mathrm{n}\not\equiv 0\left[11\right]$$$$\frac{\mathrm{n}^{\mathrm{2}} +\mathrm{4}^{\mathrm{n}} +\mathrm{7}^{\mathrm{n}}…

Question Number 192811 by Abdullahrussell last updated on 28/May/23 Answered by AST last updated on 28/May/23 $$\mathrm{\Sigma }\frac{1}{x+yz}=\mathrm{\Sigma }\frac{x}{x^2+xyz}=\frac{x}{x^2+5}+\frac{y}{y^2+5}+\frac{z}{z^2+5}$$$$=\frac{\Sigma\left({xy}^{\mathrm{2}} +\mathrm{5}{x}\right)\left({z}^{\mathrm{2}} +\mathrm{5}\right)=\Sigma\left({xy}^{\mathrm{2}}…

Question Number 192786 by MM42 last updated on 27/May/23 $$N=<aabb>\in \mathbb{N}\mathrm{\&}Nisperfectsquare$$$$findN?$$$$$$ Answered by AST last updated on 27/May/23 $$\mathrm{1100}{a}+\mathrm{11}{b}={x}^{\mathrm{2}} \Rightarrow\mathrm{11}\left(\mathrm{100}{a}+{b}\right)={x}^{\mathrm{2}}…

Question Number 192777 by York12 last updated on 26/May/23 $$\sqrt{x^2+ax-1}-\sqrt{x^2+bx-1}=\sqrt{a}-\sqrt{b}$$$$findx.$$ Commented by Frix last updated on 27/May/23 $$\mathrm{Obviously}\:{x}=\mathrm{1} \…

Question Number 61707 by hhghg last updated on 06/Jun/19 $$6^{-3}$$ Commented by Mikael last updated on 06/Jun/19 $$={\left(\frac{1}{6}\right)}^3=\frac{1}{216}$$ Terms of…