Category: Algebra

Question Number 185143 by Shrinava last updated on 17/Jan/23 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 185137 by emmanuelson123 last updated on 17/Jan/23 Answered by CElcedricjunior last updated on 17/Jan/23 $$\mathit{m}\mathit{o}\mathit{n}\mathit{t}\mathit{r}\mathit{o}\mathit{n}\mathit{s}\mathit{q}\mathit{u}\mathit{e}\mathrm{\forall }\mathit{n}\in \mathit{I}\mathit{N}$$$$\frac{\sqrt{3}}{4}[{(7+4\sqrt{3})}^{\mathit{n}}-{(7-4\sqrt{3})}^{\mathit{n}}]\equiv 0\left[6\right]$$$$\boldsymbol{{posons}}\:\boldsymbol{{p}}\left(\boldsymbol{{n}}\right)=\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}\left[\left(\mathrm{7}+\mathrm{4}\sqrt{\mathrm{3}}\right)^{\boldsymbol{{n}}} −\left(\mathrm{7}−\mathrm{4}\sqrt{\mathrm{3}}\right)^{\boldsymbol{{n}}} \right]…

Question Number 185127 by Shrinava last updated on 17/Jan/23 $$\{\begin{array}{l}\sqrt{{\mathrm{x}}^2-\frac{5}{9}+\sqrt{\mathrm{y}+{\mathrm{x}}^2-\frac{5}{9}}}=\mathrm{y}\\ \sqrt{{\mathrm{y}}^2-\frac{4}{9}+\sqrt{\mathrm{x}+{\mathrm{y}}^2-\frac{4}{9}}}=\mathrm{x}\end{array}$$$$\mathrm{Find}:\mathrm{x},\mathrm{y}=?$$ Commented by Frix last updated on 17/Jan/23…

Question Number 119580 by mathocean1 last updated on 25/Oct/20 $$\mathrm{Given}\mathrm{k}\in \mathbb{N}.$$$$1)\mathrm{justify}\mathrm{these}\mathrm{relations}:$$$$3^{2\mathrm{k}}+1\equiv 2\left[8\right]\mathrm{and}{3}^{2\mathrm{k}+1}+1\equiv 4\left[8\right].$$$$2)\mathrm{Given}\left(\mathrm{E}\right):2^{\mathrm{n}}-3^{\mathrm{m}}=1.\mathrm{n}\mathrm{and}\mathrm{m}\mathrm{are}\mathrm{unknowed}.$$$$\bullet \mathrm{Show}\mathrm{that}\mathrm{if}\mathrm{m}\mathrm{is}\mathrm{even},\left(\mathrm{E}\right)\mathrm{does}\mathrm{not}\mathrm{have}$$$$\mathrm{solution}. \…

Question Number 119576 by bemath last updated on 25/Oct/20 Answered by TANMAY PANACEA last updated on 25/Oct/20 $$x=\frac{2m}{3}y=\frac{2n}{3}z=\frac{2k}{3}$$$$\frac{4m}{3}+2n+\frac{2k}{3}=22$$$$4m+6n+2k=66$$$$\mathrm{4}\left(\mathrm{13}−{k}\right)+\mathrm{6}{n}+\mathrm{2}{k}=\mathrm{66} \…