Question Number 165774 by mathlove last updated on 08/Feb/22 Answered by Eulerian last updated on 08/Feb/22 $$\:\mathrm{let}:\:\frac{\mathrm{1}}{\mathrm{x}−\mathrm{3}}\:=\:\mathrm{y} \\ $$$$\:\mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{y}}+\mathrm{3}\:\:\Rightarrow\:\:\mathrm{y}\:=\:\frac{\mathrm{1}}{\mathrm{x}}\:+\:\mathrm{3} \\ $$$$\: \\ $$$$\:\therefore \\ $$$$\:\mathrm{f}\left(\frac{\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{x}}+\mathrm{3}−\mathrm{3}}\right)\:=\:\frac{\mathrm{1}}{\left(\frac{\mathrm{1}}{\mathrm{x}}\:+\:\mathrm{3}\right)}…
Question Number 34685 by math khazana by abdo last updated on 09/May/18 $${decompose}\:{the}\:{fraction} \\ $$$${F}\left({x}\right)=\:\:\frac{\mathrm{1}}{\left({x}+\mathrm{2}\right)\left(\:{x}^{{n}} \:\:−\mathrm{1}\right)}\:\:{with}\:{n}\:\in\:{N}^{\bigstar} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34686 by math khazana by abdo last updated on 09/May/18 $${decompose}\:{F}\left({x}\right)\:\:=\:\frac{\left(\mathrm{2}{n}\right)!}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}^{\mathrm{2}} \:−\mathrm{2}\right)….\left({x}^{\mathrm{2}} \:−{n}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34680 by math khazana by abdo last updated on 09/May/18 $${decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)\:=\:\:\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} {cos}\left(\mathrm{2}{a}\right)\:+\mathrm{1}}\:. \\ $$ Terms of Service Privacy Policy…
Question Number 165751 by cortano1 last updated on 07/Feb/22 $$\:\mathrm{x}^{\mathrm{3}} +\mathrm{6x}−\mathrm{9}=\mathrm{0}\:\Rightarrow\mathrm{x}=? \\ $$ Answered by MJS_new last updated on 08/Feb/22 $${x}_{\mathrm{1}} =\sqrt[{\mathrm{3}}]{\frac{\mathrm{9}+\sqrt{\mathrm{113}}}{\mathrm{2}}}−\sqrt[{\mathrm{3}}]{\frac{−\mathrm{9}+\sqrt{\mathrm{113}}}{\mathrm{2}}}\approx\mathrm{1}.\mathrm{20695981419} \\ $$$${x}_{\mathrm{2}} =\omega\sqrt[{\mathrm{3}}]{\frac{\mathrm{9}+\sqrt{\mathrm{113}}}{\mathrm{2}}}−\omega^{\mathrm{2}}…
Question Number 165744 by mnjuly1970 last updated on 07/Feb/22 Answered by TheSupreme last updated on 07/Feb/22 $$\lfloor{x}\rfloor−\lfloor{x}^{\mathrm{2}} \rfloor\geqslant\mathrm{0} \\ $$$$\lfloor{x}^{\mathrm{2}} \rfloor=\lfloor\left(\lfloor{x}\rfloor+\left\{{x}\right\}\right)^{\mathrm{2}} \rfloor= \\ $$$$\lfloor\lfloor{x}\rfloor^{\mathrm{2}} +\mathrm{2}\lfloor{x}\rfloor\left\{{x}\right\}+\left\{{x}\right\}^{\mathrm{2}}…
Question Number 34673 by math khazana by abdo last updated on 09/May/18 $${solve}\:\left(\frac{\mathrm{1}+{iz}}{\mathrm{1}−{iz}}\right)^{{n}} \:=\:\frac{\mathrm{1}+{itan}\alpha}{\mathrm{1}−{itan}\alpha}\:\:{with}\:−\frac{\pi}{\mathrm{2}}<\alpha<\frac{\pi}{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34669 by math khazana by abdo last updated on 09/May/18 $${let}\:{P}\left({x}\right)=\left(\mathrm{1}+{x}+{ix}^{\mathrm{2}} \right)^{{n}} \:−\left(\mathrm{1}+{x}\:−{ix}^{\mathrm{2}} \right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{P}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{factorize}\:{indide}\:{R}\left[{x}\right]\:{P}\left({x}\right). \\ $$ Commented…
Question Number 34668 by math khazana by abdo last updated on 09/May/18 $${find}\:{the}\:{roots}\:{of}?{p}\left({x}\right)\:=\:{x}^{\mathrm{2}{n}} \:−\mathrm{2}{x}^{{n}} \:{cos}\left({n}\theta\right)\:+\mathrm{1} \\ $$$$\left.\mathrm{2}\right)?{factorize}\:{p}\left({x}\right)\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 34667 by math khazana by abdo last updated on 09/May/18 $${solve}\:\:\left({x}+\mathrm{1}\right)^{{n}} \:=\:{e}^{\mathrm{2}{ina}} \:\:\:{then}\:{find}\:{the}\:{value}\:{of} \\ $$$${P}_{{n}} =\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{sin}\left({a}\:+\frac{{k}\pi}{{n}}\right) \\ $$ Terms of Service…