Question Number 28381 by Ruchinna1 last updated on 25/Jan/18 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28372 by abdo imad last updated on 24/Jan/18 $${let}\:{give}\:{w}={e}^{{i}\mathrm{2}\frac{\pi}{{n}}} \:\:\:\:.{calculate}\:\:\prod_{{l}=\mathrm{0}_{{l}\neq{k}} } ^{{n}−\mathrm{1}} \:\:\:\left({w}^{{k}} \:\:−{w}^{{l}} \right)\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 28371 by abdo imad last updated on 24/Jan/18 $${prove}\:{that}\:{x}^{\mathrm{2}} −\mathrm{2}{x}\:{cos}\theta\:+\mathrm{1}\:{divide}\:{x}^{\mathrm{2}{n}} \:−\mathrm{2}{x}^{{n}} {cos}\left({n}\theta\right)+\mathrm{1} \\ $$ Commented by abdo imad last updated on 25/Jan/18 $${let}\:{put}\:\:\:{p}_{{n}}…
Question Number 28370 by abdo imad last updated on 24/Jan/18 $$\left.\mathrm{1}\right)\:{factorizse}\:{p}\left({x}\right)\:={x}^{{n}} \:−\mathrm{1}\:\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\prod_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \:{sin}\left(\frac{{k}\pi}{{n}}\right) \\ $$$$\left.\mathrm{3}\right){find}\:{also}\:{the}\:{value}\:{of}\:\:\:\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:{sin}\left(\frac{{k}\pi}{{n}}\:+\theta\right). \\ $$ Commented by abdo…
Question Number 28369 by abdo imad last updated on 24/Jan/18 $${let}\:{give}\:{the}\:{matrice}\:\:\:{A}\:=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{1}\right.\right. \\ $$$${A}\:\in\:{M}_{\mathrm{3}} \left({R}\right)\:\:{write}\:\:{A}\:{at}\:{form}\:\:{A}=\:{I}\:+{J}\:\:\:\:{and}\:{calculate} \\ $$$${A}^{{n}} . \\ $$ Terms of Service Privacy…
Question Number 28367 by abdo imad last updated on 24/Jan/18 $${find}\:{F}\in{R}\left({x}\right)\:\:{wich}\:{verify}\:\:{F}\left({x}+\mathrm{1}\right)\:−{F}\left({x}\right)=\:\frac{{x}+\mathrm{3}}{{x}\left({x}−\mathrm{1}\right)\left({x}+\mathrm{1}\right)}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28368 by abdo imad last updated on 24/Jan/18 $${P}\:{is}\:{apolynomial}\:{from}\:{C}_{{n}} \left[{x}\right]\:{having}\:{n}\:{roots} \\ $$$$\left({x}_{{i}} \right)_{\mathrm{1}\leqslant{i}\leqslant{n}\:} \:\:\:\:{and}\:{x}_{{i}} #\:{x}_{{j}} \:{for}\:{i}#{j} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\:\sum_{{i}=\mathrm{1}} ^{{n}} \:\:\:\frac{\mathrm{1}}{{p}^{'} \left({x}_{{i}} \right)}\:\:=\mathrm{0} \\…
Question Number 28366 by abdo imad last updated on 24/Jan/18 $${let}\:{give}\:{P}\left({x}\right)=\:\alpha\left({x}−{x}_{\mathrm{1}} \right)^{{m}_{\mathrm{1}} } \left({x}−{x}_{\mathrm{2}} \right)^{{m}_{\mathrm{2}} } …..\left({x}−{x}_{{n}} \right)^{{m}_{{n}} } \\ $$$${give}\:{the}\:{decomposition}\:{of}\:{F}\left({x}\right)=\:\frac{{d}\left({P}\right)}{{P}}\:.{d}\:{mean}\:{derivative} \\ $$ Terms of…
Question Number 159436 by HongKing last updated on 17/Nov/21 Commented by cortano last updated on 17/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28364 by abdo imad last updated on 24/Jan/18 $${let}\:{give}\:{F}\left({x}\right)\:=\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{prove}\:{that}\:\exists\:{P}_{{n}} \in\:{Z}_{{n}} \left[{x}\right]\:/ \\ $$$${F}^{\left({n}\right)} \left({x}\right)=\:\:\frac{{P}_{{n}} \left({x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:\:{find}\:{a}\:{relation}\:{of}\:{recurence}\:{between}\: \\ $$$${the}\:\:{P}_{{n}} \:.{prove}\:{that}\:{all}\:{roots}\:{of}\:{P}_{{n}} \:{are}\:{reals}\:{and}\:{smples}. \\…