Category: Algebra

Question Number 158272 by HongKing last updated on 01/Nov/21 Answered by qaz last updated on 04/Nov/21 $$\Omega=\mathrm{4}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{x}^{\mathrm{2}} \mathrm{lnx}}{\mathrm{x}^{\mathrm{4}} −\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx} \\ $$$$=\mathrm{4}\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 158275 by HongKing last updated on 01/Nov/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{x}^{\mathrm{32}} \:+\:\mathrm{x}^{\mathrm{16}} \:+\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{2}\:\sqrt{\mathrm{2}}\:\mathrm{x}^{\mathrm{12}} \:\mathrm{y} \\ $$$$ \\ $$ Answered by mindispower last updated…

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…