Category: Algebra

Question Number 192862 by Red1ight last updated on 30/May/23 $$\mathrm{Solve}\mathrm{for}x$$$$x^3-115x+150=0$$ Answered by Frix last updated on 30/May/23 $$\left({x}−\mathrm{10}\right)\left({x}^{\mathrm{2}} +\mathrm{10}{x}−\mathrm{15}\right)=\mathrm{0} \…

Question Number 192852 by York12 last updated on 29/May/23 $$$$$$findthedomainofthefunction$$$$f\left(x\right)=\frac{1}{\sqrt{x^2-{\left\{x\right\}}^2}}where\{.\}isthefractionalpartfunction.$$ Commented by York12 last updated on 30/May/23…

Question Number 192851 by MATHEMATICSAM last updated on 29/May/23 $$\mathrm{Solve}:$$$$\frac{{\log }_{a^2\sqrt{x}}a}{{\log }_{2x}a}+{\log }_{ax}a.{\log }_{\frac{1}{a}}2x=0$$ Commented by Frix last updated on…

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}}…