Menu Close

Category: Algebra

let-P-x-1-ix-n-1-ni-with-x-real-and-n-integr-natural-1-find-the-roots-of-P-x-2-factorize-P-x-inside-C-x-3-factorize-P-x-inside-R-x-4-decompose-the-fraction-F-x-P-1-x-P-x-

Question Number 57947 by maxmathsup by imad last updated on 14/Apr/19 $${let}\:{P}\left({x}\right)=\left(\mathrm{1}+{ix}\right)^{{n}} −\mathrm{1}−{ni}\:\:\:\:{with}\:{x}\:{real}\:{and}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right)\:{factorize}\:{P}\left({x}\right)\:{inside}\:{R}\left[{x}\right] \\ $$$$\left.\mathrm{4}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)\:=\frac{{P}^{\left(\mathrm{1}\right)} \left({x}\right)}{{P}\left({x}\right)}\:{inside}\:{C}\left({x}\right) \\ $$$${P}^{\left(\mathrm{1}\right)} \:{is}\:{the}\:{derivative}\:{of}\:{P}\:.…

Suppose-G-and-H-are-groups-Take-homomorphism-G-H-Suppose-g-G-g-n-then-g-n-Does-g-G-g-g-G-H-

Question Number 189013 by Pengu last updated on 10/Mar/23 $$\mathrm{Suppose}\:\left({G},\:\centerdot\:\right)\:\mathrm{and}\:\left({H},\:\ast\:\right)\:\mathrm{are}\:\mathrm{groups}. \\ $$$$\mathrm{Take}\:\mathrm{homomorphism}\:\phi\::\:{G}\:\rightarrow\:{H}. \\ $$$$\mathrm{Suppose}\:\exists{g}\in{G}\::\:\mid{g}\mid\:=\:{n},\:\mathrm{then}\:\mid\phi\left({g}\right)\mid\:\leqslant\:{n}. \\ $$$$\: \\ $$$$\mathrm{Does}\:\forall{g}\in{G},\:\mid{g}\mid\:=\:\mid\phi\left({g}\right)\mid\:\Rightarrow\:{G}\:\cong\:{H}\:? \\ $$ Answered by aleks041103 last updated…

solve-2-3-2-11-3-

Question Number 57930 by Jaiden2019 last updated on 14/Apr/19 $$\mathrm{solve}\:\mathrm{2}.\mathrm{3}\left(\frac{\mathrm{2}}{\mathrm{11}}+\mathrm{3}\right) \\ $$ Answered by peter frank last updated on 14/Apr/19 $$\mathrm{2}.\mathrm{3}\left(\frac{\mathrm{2}+\mathrm{33}}{\mathrm{11}}\right) \\ $$$$\mathrm{2}.\mathrm{3}×\left(\frac{\mathrm{35}}{\mathrm{11}}\right) \\ $$$$\frac{\mathrm{80}.\mathrm{5}}{\mathrm{11}}…

find-the-radii-of-all-circles-with-center-C-tangenting-the-curve-h-C-5-1-h-x-2-y-2-1-

Question Number 123426 by MJS_new last updated on 25/Nov/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{radii}\:\mathrm{of}\:\mathrm{all}\:\mathrm{circles}\:\mathrm{with}\:\mathrm{center}\:{C} \\ $$$$\mathrm{tangenting}\:\mathrm{the}\:\mathrm{curve}\:{h} \\ $$$${C}=\begin{pmatrix}{\mathrm{5}}\\{\mathrm{1}}\end{pmatrix} \\ $$$${h}:\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{1} \\ $$ Commented by ajfour last updated…