Question Number 161666 by mathlove last updated on 21/Dec/21 $${if}\:\:\frac{{g}\left(\mathrm{5}\right){f}\left(\mathrm{5}\right)}{{g}\left(\mathrm{5}\right)+{f}\left(\mathrm{5}\right)}=\mathrm{1}\:\:\:{then}\frac{{f}\left(\mathrm{4}\right)+{g}\left(\mathrm{4}\right)}{{f}\left(\mathrm{4}\right)+\mathrm{1}}=? \\ $$$${when}\:{is}\:\:\:\:\:{Gis}\:{a}\:{I}\:{function}\:\:{and}\:{F}\:{is}\:{a}\:{constant} \\ $$ Commented by mr W last updated on 21/Dec/21 $${the}\:{language}\:{is}\:{not}\:{clear}. \\ $$$${what}\:{are}\:{G}\:{and}\:{F}?…
Question Number 30589 by abdo imad last updated on 23/Feb/18 $${let}\:{U}_{{n}} =\:\left\{{z}\in{C}\:/\:{z}^{{n}} =\mathrm{1}\right\}\:\:{find} \\ $$$${S}=\:\sum_{{z}\in{U}_{{n}} } \:\:\frac{{z}}{\left({x}−{z}\right)^{\mathrm{2}} }\:\:. \\ $$ Terms of Service Privacy Policy…
Question Number 30590 by abdo imad last updated on 23/Feb/18 $${decompose}\:{sur}\:{R}\left[{x}\right]\:\:{x}^{\mathrm{2}{n}+\mathrm{1}} \:−\mathrm{1}. \\ $$ Answered by sma3l2996 last updated on 23/Feb/18 $${let}\:{P}\left({x}\right)={x}^{\mathrm{2}{n}+\mathrm{1}} −\mathrm{1} \\ $$$$\alpha_{{k}}…
Question Number 30588 by abdo imad last updated on 23/Feb/18 $$\left({n}_{{k}} \right)_{\mathrm{1}\leqslant{k}\leqslant{n}} \:{is}\:{a}\:{family}\:{of}\:{integrs}\:{numbers}\:{let}\:{put} \\ $$$${p}\left({x}\right)=\sum_{{k}=\mathrm{1}} ^{{n}} \:{x}^{{n}_{{k}} } \:\:\:{and}\:{q}\left({x}\right)=\:\sum_{{j}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{x}^{{j}} \: \\ $$$${if}\:{n}_{{k}} \equiv{k}−\mathrm{1}\left[{n}\right]\:{prove}\:{that}\:{q}\:{divide}\:{p}.…
Question Number 30587 by abdo imad last updated on 23/Feb/18 $${find}\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\left(−\mathrm{1}\right)^{{k}} \:{cos}^{{n}} \left(\frac{{k}\pi}{{n}}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30586 by abdo imad last updated on 23/Feb/18 $${let}\:{p}=\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+….+{x}^{\mathrm{2}^{{n}+\mathrm{1}} −\mathrm{1}} \:{and}\:\:{q}=\:\mathrm{1}+{x}^{\mathrm{2}^{{n}} } \\ $$$${find}\:\alpha=\:\frac{{p}}{{q}}\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 30583 by abdo imad last updated on 23/Feb/18 $${decompose}\:{F}\:=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{{n}} }\:{inside}\:{C}\left[{x}\right].{n}\:{from}\:{N}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30581 by abdo imad last updated on 23/Feb/18 $${decompose}\:{inside}\:{C}\left[{x}\right]\:{F}=\:\:\frac{\mathrm{1}}{\left({x}+{iy}\right)^{{n}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30582 by abdo imad last updated on 23/Feb/18 $${x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:{x}_{\mathrm{3}\:} \:{are}\:{roots}\:{of}\:{the}\:{polynomial}\:{x}^{\mathrm{3}} \:−{x}+\mathrm{1}\:{find} \\ $$$${the}\:{polynomial}\:{wich}\:{have}\:{for}\:{roots}\:{x}_{\mathrm{1}} ^{\mathrm{3}} \:,{x}_{\mathrm{2}} ^{\mathrm{3}} \:{and}\:{x}_{\mathrm{3}} ^{\mathrm{3}} \:\:. \\ $$…
Question Number 30579 by abdo imad last updated on 23/Feb/18 $${decompose}\:{inside}\:{C}\left[{x}\right]\:{F}=\:\frac{{x}^{{n}} −\mathrm{1}}{{x}^{\mathrm{2}{n}} −\mathrm{1}}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com