Category: Algebra

Question Number 161567 by HongKing last updated on 19/Dec/21 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)\mathrm{be}$$$$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{x}}{\ln (1-\mathrm{x})}$$$$\mathrm{prove}\mathrm{there}\mathrm{exists}\mathrm{a}\mathrm{sequence}\left\{{\mathrm{a}}_{\mathbf{k}}\right\}\mathrm{such}\mathrm{that}$$$$\mathrm{D}\left[\mathrm{f}\left(\mathrm{x}\right)\right]=\left[\underset{0}{\sum ^{\mathrm{\infty }}}{\mathrm{a}}_{\mathbf{k}}{\mathrm{x}}^{\mathbf{k}}\right]{\left[\mathrm{f}\left(\mathrm{x}\right)\right]}^2$$ Answered by…

Question Number 161563 by HongKing last updated on 19/Dec/21 $$\mathrm{Solve}\mathrm{the}\mathrm{equation}:$$$$\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\dots }}}=\mathrm{x}\cdot \sqrt{\mathrm{x}\cdot \sqrt{\mathrm{x}\cdot \sqrt{\mathrm{x}\cdot \dots }}}$$$$\mathrm{where},\mathrm{x}>0$$ Answered by MJS_new last updated on 20/Dec/21 $$\mathrm{lhs}=\left(\mathrm{lhs}−{x}\right)^{\mathrm{2}} \wedge\mathrm{lhs}\geqslant{x}\:\Rightarrow\:\mathrm{lhs}=\frac{\mathrm{2}{x}+\mathrm{1}+\sqrt{\mathrm{4}{x}+\mathrm{1}}}{\mathrm{2}}…

Question Number 96021 by SmNayon11 last updated on 29/May/20 $$\mathrm{if}\mathrm{p}\mathrm{and}\mathrm{q}\mathrm{are}\mathrm{two}\mathrm{complex}\mathrm{number}$$$$\mathrm{and}\mathrm{p}\times \mathrm{q}=\mathrm{m},\mathrm{m}\mathrm{is}\mathrm{a}\mathrm{real}\mathrm{number}.$$$$$$$$\mathrm{is}\mathrm{there}\mathrm{always}\mathrm{exists}\mathrm{a}{\mathrm{p}}^{\frac{1}{3}}\mathrm{and}{\mathrm{q}}^{\frac{1}{3}}$$$$(\mathrm{we}\mathrm{know}{\mathrm{p}}^{\frac{1}{3}}\mathrm{and}{\mathrm{q}}^{\frac{1}{3}}\mathrm{each}\mathrm{has}\mathrm{actually}$$$$3\mathrm{values})$$$$\mathrm{such}\:\mathrm{that}\:\mathrm{p}^{\frac{\mathrm{1}}{\mathrm{3}}}…

Question Number 161527 by mnjuly1970 last updated on 19/Dec/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 95964 by i jagooll last updated on 29/May/20 $$\{\begin{array}{l}{\mathrm{x}}^2+{\mathrm{y}}^2=13\\ {2\mathrm{x}}^2+3\mathrm{y}={2\mathrm{xy}}^2\end{array}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com