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Category: Algebra

x-3-6x-9-0-x-

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-165744

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}}…

let-P-x-1-x-ix-2-n-1-x-ix-2-n-1-find-the-roots-of-P-x-2-factorize-inside-C-x-P-x-3-factorize-indide-R-x-P-x-

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…

7-2-7-2-7-2-7-2-7-

Question Number 100193 by bobhans last updated on 25/Jun/20 $$\sqrt{\mathrm{7}+\mathrm{2}\sqrt{\mathrm{7}−\mathrm{2}\sqrt{\mathrm{7}+\mathrm{2}\sqrt{\mathrm{7}−\mathrm{2}\sqrt{\mathrm{7}+…}}}}}\:? \\ $$ Commented by bobhans last updated on 25/Jun/20 $${x}\:=\sqrt{\mathrm{7}+\mathrm{2}{y}}\:;\:\mathrm{y}=\sqrt{\mathrm{7}−\mathrm{2}{x}} \\ $$$$\Leftrightarrow{x}^{\mathrm{2}} \:=\:\mathrm{7}+\mathrm{2}{y}\:\_\left(\mathrm{1}\right) \\ $$$$\Leftrightarrow\mathrm{y}^{\mathrm{2}}…