Question Number 162367 by cortano last updated on 29/Dec/21 $$\:\:{Let}\:{x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,{x}_{\mathrm{3}} \:{be}\:{the}\:{roots}\:{of}\:{the}\: \\ $$$${equation}\:{x}^{\mathrm{3}} +\mathrm{3}{x}+\mathrm{5}=\mathrm{0}\:.\:{Then}\:{the} \\ $$$${value}\:{of}\:{expression}\:\left({x}_{\mathrm{1}} +\frac{\mathrm{1}}{{x}_{\mathrm{1}} }\right)\left({x}_{\mathrm{2}} +\frac{\mathrm{1}}{{x}_{\mathrm{2}} }\right)\left({x}_{\mathrm{3}} +\frac{\mathrm{1}}{{x}_{\mathrm{3}} }\right)\:{is} \\…
Question Number 96829 by bobhans last updated on 05/Jun/20 $$\mathrm{If}\:\mathrm{2f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{2}} .\:\mathrm{determine}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$ Commented by john santu last updated on 05/Jun/20 $$\mathrm{replace}\:\mathrm{x}\:\mathrm{by}\:\mathrm{1}−\mathrm{x}\:\mathrm{into}\:\mathrm{eq}\left(\mathrm{1}\right) \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2f}\left(\mathrm{1}−\mathrm{x}\right)\:+\mathrm{f}\left(\mathrm{x}\right)\:=\:\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} \\…
Question Number 31290 by jasno91 last updated on 05/Mar/18 Commented by Tinkutara last updated on 05/Mar/18 $$\frac{\mathrm{9}}{\mathrm{4}}\:{m} \\ $$ Answered by Joel578 last updated on…
Question Number 31286 by 6123 last updated on 05/Mar/18 $${Find}\:{all}\:{set}\:{of}\:{ordered}\:{triple}/{s}\:\left({x},{y},{z}\right),\:\:{x},{y},{z}\in\Re,\:{such}\:{that} \\ $$$${x}−{y}=\mathrm{1}−{z} \\ $$$$\mathrm{3}\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)=\mathrm{5}\left(\mathrm{1}−{z}^{\mathrm{2}} \right) \\ $$$$\mathrm{7}\left({x}^{\mathrm{3}} −{y}^{\mathrm{3}} \right)=\mathrm{19}\left(\mathrm{1}−{z}^{\mathrm{3}} \right). \\ $$$${Please}\:{show}\:{your}\:{solution}. \\…
Question Number 96821 by bobhans last updated on 05/Jun/20 $$\begin{cases}{\frac{\mathrm{u}^{\mathrm{2}} }{\mathrm{v}}\:+\:\frac{\mathrm{v}^{\mathrm{2}} }{\mathrm{u}}\:=\:\mathrm{12}}\\{\frac{\mathrm{1}}{\mathrm{u}}\:+\:\frac{\mathrm{1}}{\mathrm{v}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}}\end{cases}\:.\:\mathrm{find}\:\mathrm{u}\:\mathrm{and}\:\mathrm{v}\:? \\ $$ Answered by john santu last updated on 05/Jun/20 Commented by bobhans…
Question Number 162338 by HongKing last updated on 28/Dec/21 $$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:-\:\mathrm{3}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)\:-\:\mathrm{4y}\:=\:\mathrm{tan}\left(\mathrm{x}\right)\mathrm{log}\left(\mathrm{cos}\left(\mathrm{x}\right)\right) \\ $$ Answered by Ar Brandon last updated on 29/Dec/21 $$\mathrm{y}''−\mathrm{3y}'−\mathrm{4y}=\mathrm{tan}{x}\centerdot\mathrm{ln}\left(\mathrm{cos}{x}\right) \\ $$$$\mathrm{For}\:\mathrm{y}_{\mathrm{gh}}…
Question Number 31259 by rahul 19 last updated on 04/Mar/18 Commented by rahul 19 last updated on 04/Mar/18 $$\mathrm{y}=\:\left(\mathrm{2}{x}+\mathrm{3}\right)\:+\:\frac{\mathrm{7}}{\left({x}+\mathrm{3}\right)}\:. \\ $$$$\mathrm{this}\:\mathrm{is}\:\mathrm{hint}\:\mathrm{given}! \\ $$ Commented by…
Question Number 162305 by mathlove last updated on 28/Dec/21 $${proof}\:{that} \\ $$$$\mathrm{2}^{{n}+\mathrm{1}} >\left({n}+\mathrm{2}\right)\mathrm{sin}\:{n} \\ $$ Answered by aleks041103 last updated on 28/Dec/21 $${sin}\left({n}\right)\leqslant\mathrm{1} \\ $$$$\Rightarrow\left({n}+\mathrm{2}\right){sin}\left({n}\right)\leqslant{n}+\mathrm{2}…
Question Number 31214 by Tinkutara last updated on 03/Mar/18 Commented by abdo imad last updated on 03/Mar/18 $${we}\:{have}\:{u}_{{n}+\mathrm{1}} =\mathrm{3}{u}_{{n}} −\mathrm{2}\:{u}_{{n}−\mathrm{1}\:} \Rightarrow{u}_{{n}+\mathrm{2}} \:−\mathrm{3}{u}_{{n}+\mathrm{1}} \:+\mathrm{2}{u}_{{n}} =\mathrm{0} \\…
Question Number 96749 by student work last updated on 04/Jun/20 $$\mathrm{how}\:\mathrm{we}\:\mathrm{can}\:\mathrm{calclate}\:\mathrm{triple}\:\mathrm{factorial}? \\ $$ Answered by Rio Michael last updated on 04/Jun/20 $$\mathrm{The}\:\mathrm{tripple}\:\mathrm{factorial}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{as}\: \\ $$$$\:{n}!!!\:=\:{n}\left({n}−\mathrm{3}\right)\left({n}−\mathrm{6}\right)…\mathrm{3},\:\:{n}\left({n}−\mathrm{3}\right)\left({n}−\mathrm{6}\right)…\mathrm{4}\ast\mathrm{1} \\…