Category: Algebra

Question Number 92727 by I want to learn more last updated on 08/May/20 $$\mathrm{Solve}:\:\:\:\:\:\mathrm{x}^{\mathrm{y}} \:\:=\:\:\mathrm{y}^{\mathrm{x}} \:\:\:\:\:…….\:\:\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}^{\mathrm{x}} \:\:=\:\:\mathrm{15}^{\mathrm{y}} \:\:\:\:……\:\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\mathrm{x}\:\:\neq\:\:\mathrm{y},\:\:\:\:\:\:\:\mathrm{x},\:\:\mathrm{y}\:\in\:\mathbb{R} \\ $$ Answered…

Question Number 92717 by mr W last updated on 08/May/20 Commented by i jagooll last updated on 09/May/20 $$\left(\mathrm{1}\right)\:\mathrm{x}^{\mathrm{3}} +\mathrm{9x}^{\mathrm{2}} \mathrm{y}\:=\:\mathrm{10} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{27y}^{\mathrm{3}} +\mathrm{27xy}^{\mathrm{2}} \:=\:\mathrm{54}…

Question Number 158245 by HongKing last updated on 01/Nov/21 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\frac{\left(\mathrm{x}-\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{x}}\:+\:\frac{\mathrm{x}+\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\:\geqslant\:\sqrt{\mathrm{2}}\:\:;\:\:\forall\mathrm{x}>\mathrm{0} \\ $$$$ \\ $$ Answered by mindispower last updated on 02/Nov/21…

Question Number 158220 by ajfour last updated on 01/Nov/21 $$\:\:\:{source}:\:{myself} \\ $$$$\:{x}^{\mathrm{5}} +\mathrm{3}{cx}^{\mathrm{2}} −{x}−\mathrm{5}{c}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 158187 by HongKing last updated on 31/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\sqrt{\mathrm{x}}\:-\:\mathrm{y}^{\mathrm{5}} \:=\:\mathrm{3}}\\{\sqrt[{\mathrm{5}}]{\sqrt{\mathrm{x}}\:-\:\mathrm{3}}\:-\:\sqrt[{\mathrm{5}}]{\mathrm{y}^{\mathrm{5}} \:+\:\mathrm{6}}\:=\:-\:\mathrm{1}}\end{cases}\: \\ $$$$ \\ $$ Answered by MJS_new last updated on 31/Oct/21…