Category: Algebra

Question Number 160712 by HongKing last updated on 05/Dec/21 $$\mathrm{Solve}\mathrm{for}\mathrm{real}\mathrm{numbers}:$$$${\left(\frac{{\mathrm{x}}^2+{3\mathrm{n}}^2}{{4\mathrm{n}}^2}\right)}^4=\frac{2}{\mathrm{n}}\mathrm{y}-1;{\left(\frac{{\mathrm{x}}^2+{3\mathrm{n}}^2}{{4\mathrm{n}}^2}\right)}^4=\frac{2}{\mathrm{n}}\mathrm{z}-1$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{3n}^{\mathrm{2}} }{\mathrm{4n}^{\mathrm{2}} }\right)^{\mathrm{4}}…

Question Number 160706 by HongKing last updated on 05/Dec/21 Answered by mr W last updated on 05/Dec/21 $$S_n=\underset{k=1}{\sum ^n}\sin \left(\frac{k}{n^3}\right)$$$${T}_{{n}} =\underset{{k}=\mathrm{1}}…

Question Number 95167 by Rio Michael last updated on 23/May/20 $$\mathrm{the}\mathrm{first}\mathrm{term}\mathrm{in}\mathrm{a}\mathrm{geometric}\mathrm{series}\mathrm{is}\frac{(2x+7)}{2x-5}\mathrm{and}\mathrm{the}\mathrm{common}\mathrm{ratio}\mathrm{is}$$$$\frac{(2x-5)}{2x+7}\mathrm{find}\mathrm{the}\mathrm{set}\mathrm{of}\mathrm{values}\mathrm{of}x\mathrm{for}\mathrm{which}\mathrm{all}\mathrm{the}\mathrm{terms}\mathrm{are}\mathrm{possible}.$$ Commented by john santu last updated on 23/May/20 $$\left(\mathrm{1}\right)\:\mathrm{x}\:\neq\:\frac{\mathrm{5}}{\mathrm{2}}\:\wedge\:\mathrm{x}\:\neq\:−\frac{\mathrm{7}}{\mathrm{2}}\: \…

Question Number 95159 by i jagooll last updated on 23/May/20 $$\sqrt[3]{8-\mathrm{x}}+\sqrt{\mathrm{x}}=2$$ Commented by hknkrc46 last updated on 23/May/20 $$★\sqrt[2n+1]{f\left(x\right)}\Rightarrow \mathrm{\forall }f\left(x\right)\in \mathbb{R}\to f\left(x\right)⩾0\vee f\left(x\right)⩽0$$$$\bigstar\sqrt[{\mathrm{2}{n}}]{{f}\left({x}\right)}\:\Rightarrow\:\forall{f}\left({x}\right)\:\in\:\mathbb{R}^{+} \:\rightarrow\:{f}\left({x}\right)\geqslant\mathrm{0} \…

Question Number 160695 by HongKing last updated on 04/Dec/21 Terms of Service Privacy Policy Contact: info@tinkutara.com