Question Number 156107 by cortano last updated on 08/Oct/21 $$\:\:\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}+\mathrm{1}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2019}}\right)^{\mathrm{2019}} \\ $$ Commented by mr W last updated on 08/Oct/21 $$\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}+\mathrm{1}} \\ $$$$=\left(\frac{{x}+\mathrm{1}}{{x}}\right)^{{x}+\mathrm{1}} \\…
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Question Number 25025 by tawa tawa last updated on 01/Dec/17 $$\mathrm{If}\:\:\:\:\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \:+\:\mathrm{d}^{\mathrm{4}} \:=\:\mathrm{16},\:\:\mathrm{prove}\:\mathrm{that}:\:\:\mathrm{a}^{\mathrm{5}} \:+\:\mathrm{b}^{\mathrm{5}} \:+\:\mathrm{c}^{\mathrm{5}} \:+\:\mathrm{d}^{\mathrm{5}} \:\leqslant\:\mathrm{32} \\ $$$$\mathrm{for}\:\:\mathrm{a},\:\mathrm{b},\:\mathrm{c},\:\mathrm{d}\:\in\:\mathbb{R} \\ $$ Answered by…
Question Number 90557 by I want to learn more last updated on 24/Apr/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{enclose}\:\mathrm{by}\:\mathrm{the}\:\mathrm{line}\:\:\:\mathrm{y}\:\:=\:\:\mathrm{x}\:\:−\:\:\mathrm{1}\:\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{parabola}\:\:\:\mathrm{y}^{\mathrm{2}} \:\:=\:\:\mathrm{2x}\:\:+\:\:\mathrm{6} \\ $$ Commented by I want to learn…
Question Number 25023 by Tinkutara last updated on 01/Dec/17 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{which} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{functional}\:\mathrm{equation} \\ $$$$\mathrm{2}{f}\left({x}\right)\:+\:{f}\left(\mathrm{1}\:−\:{x}\right)\:=\:{x}^{\mathrm{2}} \:+\:\mathrm{1},\:\forall\:{x}\:\in\:{R} \\ $$$$\mathrm{and}\:{g}\left({x}\right)\:=\:\mathrm{3}{f}\left({x}\right)\:+\:\mathrm{1}.\:\mathrm{The}\:\mathrm{range}\:\mathrm{of} \\ $$$$\phi\left({x}\right)\:=\:{g}\left({x}\right)\:+\:\frac{\mathrm{1}}{{g}\left({x}\right)\:+\:\mathrm{1}}\:\mathrm{is} \\ $$ Answered by prakash jain…
Question Number 156085 by MathSh last updated on 07/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\left(\mathrm{sin2x}\:+\:\mathrm{4cos}^{\mathrm{2}} \mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{cos5x}\:-\:\mathrm{cosx}\right)<\mathrm{0} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 156086 by MathSh last updated on 07/Oct/21 $$\psi^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{1}}{\mathrm{6}}\right)\:-\:\psi^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{5}}{\mathrm{6}}\right)\:=\:\mathrm{10}\psi^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{1}}{\mathrm{3}}\right)\:-\:\frac{\mathrm{20}}{\mathrm{3}}\pi^{\mathrm{2}} \\ $$$$ \\ $$ Commented by puissant last updated on 09/Oct/21 $$\psi^{\left(\mathrm{1}\right)}…
Question Number 90550 by jagoll last updated on 24/Apr/20 $${x}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\:=\:\mathrm{527}\: \\ $$$$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left({x}−\mathrm{3}\right)\left({x}−\mathrm{4}\right)\:?\: \\ $$ Commented by jagoll last updated on 24/Apr/20 Commented by…
Question Number 25001 by Tinkutara last updated on 30/Nov/17 $$\mathrm{If}\:{x},\:{y}\:>\:\mathrm{0},\:\mathrm{then}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} \:+\:\frac{\mathrm{2}}{{x}}\:−\:\mathrm{2}{x}\:+\:\mathrm{2}{y}^{\mathrm{2}} \:+\:\frac{\mathrm{2}}{{y}}\:−\:\mathrm{2}{y}\:+\:\mathrm{2}\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to} \\ $$ Commented by prakash jain last updated on…
Question Number 156061 by mathlove last updated on 07/Oct/21 Answered by TheSupreme last updated on 07/Oct/21 $$\mathrm{2}{xy}=\mathrm{3}{x}+\mathrm{2}{y} \\ $$$${xz}=−\mathrm{20}{x}+\mathrm{12}{z} \\ $$$$\mathrm{2}{yz}=−\mathrm{12}{y}+\mathrm{15}{z} \\ $$$$ \\ $$$${y}\left(\mathrm{2}{z}+\mathrm{12}\right)=\mathrm{15}{z}…