Question Number 30599 by abdo imad last updated on 23/Feb/18 $${decompose}\:{inside}\:{C}\left({x}\right)\:\:{F}=\:\frac{\mathrm{1}}{\left({x}−\mathrm{1}\right)\left({x}^{{n}} \:−\mathrm{1}\right)}\:. \\ $$ Commented by abdo imad last updated on 25/Feb/18 $${the}\:{roots}\:{of}\:{z}^{{n}} \:−\mathrm{1}=\mathrm{0}\:{are}\:{the}\:{complex}\:{z}_{{k}} =\:{e}^{{i}\frac{\mathrm{2}{k}\pi}{{k}}}…
Question Number 30600 by abdo imad last updated on 23/Feb/18 $${let}\:{w}_{{k}} ={e}^{{i}\frac{\mathrm{2}{k}\pi}{{n}}} \:\:\:\:{find}\:{A}=\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left({a}\:+{bw}_{{k}} \:\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 161668 by mnjuly1970 last updated on 21/Dec/21 Answered by mr W last updated on 21/Dec/21 $$\frac{\mathrm{sin}^{\mathrm{2}} \:{x}}{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \:{x}}=\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \:{x} \\ $$$$\mathrm{sin}^{\mathrm{4}} \:{x}+\mathrm{sin}^{\mathrm{2}} \:{x}−\mathrm{1}=\mathrm{0}…
Question Number 30598 by abdo imad last updated on 23/Feb/18 $${prove}\:{that}\:{it}\:{exist}\:{one}\:{polynomial}\:{p}/ \\ $$$${p}\left({cosx}\right)={cos}\left({nx}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right)\:. \\ $$ Commented by abdo imad last updated on 27/Feb/18 $${we}\:{have}\:{by}\:{moivre}\:{formula}\: \\…
Question Number 30596 by abdo imad last updated on 23/Feb/18 $${find}\:{all}\:{polynomial}\:{wich}\:{verify}\: \\ $$$${p}\left({x}^{\mathrm{2}} \right)\:+{p}\left({x}\right){p}\left({x}+\mathrm{1}\right)=\mathrm{0}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30597 by abdo imad last updated on 23/Feb/18 $${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{x}\right)^{{m}} \:−{e}^{\mathrm{2}{imx}} \left(\mathrm{1}−{x}\right)^{{m}} \:{factorize}\:{p}\left({x}\right) \\ $$$${inside}\:{C}\left[{x}\right]. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30594 by abdo imad last updated on 23/Feb/18 $${let}\:{p}\left({x}\right)={x}^{\mathrm{3}} \:+\mathrm{1}\:{and}\:{q}\left({x}\right)={x}^{\mathrm{4}} \:+\mathrm{1}\:{prove}\:{that} \\ $$$${D}\left({p},{q}\right)=\mathrm{1}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 96131 by bemath last updated on 30/May/20 $$\sqrt[{\mathrm{3}\:\:}]{\left({x}+\mathrm{4}\right)^{\mathrm{2}} }\:+\:\mathrm{4}\:\sqrt[{\mathrm{3}\:\:}]{\left({x}−\mathrm{3}\right)^{\mathrm{2}} }\:+\:\mathrm{5}\:\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{2}} +{x}−\mathrm{12}}\:=\:\mathrm{0} \\ $$ Answered by john santu last updated on 30/May/20 $$\mathrm{let}\:\sqrt[{\mathrm{3}\:\:}]{{x}+\mathrm{4}}\:=\:{u}\:\&\:\sqrt[{\mathrm{3}\:\:}]{{x}−\mathrm{3}}\:=\:{v}\: \\…
Question Number 30593 by abdo imad last updated on 23/Feb/18 $${factorize}\:{inside}\:{C}\left[{x}\right]\:{p}\left({x}\right)=\left(\mathrm{1}+{i}\frac{{x}}{{n}}\right)^{{n}} \:−\left(\mathrm{1}−{i}\frac{{x}}{{n}}\right)^{{n}} . \\ $$ Answered by sma3l2996 last updated on 23/Feb/18 $${p}\left({x}\right)=\left(\mathrm{1}+{ix}/{n}\right)^{{n}} −\left(\mathrm{1}−{ix}/{n}\right)^{{n}} \\…
Question Number 30592 by abdo imad last updated on 23/Feb/18 $${let}\:{p}\left({x}\right)={x}^{\mathrm{2}{n}} \:−\mathrm{2}{cos}\alpha\:{x}^{{n}} \:+\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{roots}\:{lf}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right){factorize}\:{p}\left({x}\right)\:{inside}\:{R}\left[{x}\right]. \\ $$ Answered by sma3l2996 last…