Category: Algebra

Question Number 199183 by hardmath last updated on 29/Oct/23 $$\mathrm{B},\mathrm{O},\mathrm{M}\:-\:\mathrm{Each}\:\mathrm{is}\:\mathrm{a}\:\mathrm{distinct}\:\mathrm{positive} \\ $$$$\mathrm{integer} \\ $$$$\mathrm{If}\:\:\:\mathrm{B}\:\centerdot\:\mathrm{O}\:\centerdot\:\mathrm{M}\:=\:\mathrm{223} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{max}\left(\mathrm{B}\:+\:\mathrm{O}\:+\:\mathrm{M}\right)=? \\ $$ Answered by mr W last updated on…

Question Number 199165 by hardmath last updated on 28/Oct/23 Answered by Frix last updated on 28/Oct/23 $$−\mathrm{1}=\mathrm{e}^{\mathrm{i}\pi} \\ $$$$\left(−\mathrm{1}\right)^{\pi} =\mathrm{e}^{\mathrm{i}\pi^{\mathrm{2}} } = \\ $$$$=\mathrm{cos}\:\pi^{\mathrm{2}} \:+\mathrm{i}\:\mathrm{sin}\:\pi^{\mathrm{2}}…

Question Number 199135 by hardmath last updated on 28/Oct/23 $$\mathrm{a}\:+\:\frac{\mathrm{1}}{\mathrm{a}}\:=\:\mathrm{3} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a}^{\mathrm{5}} \:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{5}} }\:\:=\:\:? \\ $$ Answered by som(math1967) last updated on 28/Oct/23 $$\mathrm{123} \\…

Question Number 199159 by cortano12 last updated on 28/Oct/23 $$\:\sqrt[{\mathrm{4}}]{\mathrm{8}\left(\mathrm{x}+\mathrm{1}\right)}\:+\sqrt[{\mathrm{4}}]{\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}}\:=\sqrt[{\mathrm{4}}]{\mathrm{5}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} −\mathrm{3}}\: \\ $$$$\:\mathrm{x}=? \\ $$ Answered by Frix last updated on 28/Oct/23 $$\mathrm{You}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\…

Question Number 199109 by mnjuly1970 last updated on 28/Oct/23 $$ \\ $$$$\:{Q}:\:\:\:\:\alpha\:,\:\beta\:,\gamma\:{are}\:{the}\:{roots}\:{of}\:{the}\:{following} \\ $$$$\:\:\:\:\:{equation}\:.\:{find}\:{the}\:{value}\:{of}: \\ $$$$ \\ $$$$\:\:\:\:\:{Eq}^{\:{n}} \::\:\:\:{x}^{\:\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} \:+\:{x}\:+\:\mathrm{2}=\mathrm{0} \\ $$$$\:\:\:{E}\:=\:\frac{\alpha}{\beta\:+\gamma}\:+\frac{\beta}{\alpha\:+\gamma}\:+\frac{\gamma}{\alpha+\:\beta} \\ $$$$…