Question Number 161704 by HongKing last updated on 21/Dec/21 $$\mathrm{let}\:\:\mathrm{n}\in\mathbb{N}\:\:\mathrm{fixed}\:,\:\mathrm{solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\left[\mathrm{x}\right]\left\{\mathrm{x}\right\}=\mathrm{nx} \\ $$ Commented by mr W last updated on 21/Dec/21 $${two}\:{solutions}: \\ $$$${x}=−\frac{\mathrm{1}}{{n}+\mathrm{1}},\:\mathrm{0}…
Question Number 96171 by bemath last updated on 30/May/20 $$\left(\mathrm{4}+\sqrt{\mathrm{15}}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} −\left(\mathrm{4}−\sqrt{\mathrm{15}}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} =\:\mathrm{k}\sqrt{\mathrm{6}} \\ $$$$\mathrm{find}\:\mathrm{k}\: \\ $$ Commented by bobhans last updated on 30/May/20 $$\mathrm{let}\sqrt{\mathrm{4}+\sqrt{\mathrm{15}}}\:=\:\mathrm{u}\:\&\:\sqrt{\mathrm{4}−\sqrt{\mathrm{15}}}\:=\:\mathrm{v}\: \\…
Question Number 30627 by Tinkutara last updated on 23/Feb/18 Answered by ajfour last updated on 23/Feb/18 $${y}=\left({x}+\mathrm{2}\right)^{\mathrm{3}} \left(\mathrm{2}−{x}\right)^{\mathrm{4}} \\ $$$$\frac{{dy}}{{dx}}=\mathrm{3}\left({x}+\mathrm{2}\right)^{\mathrm{2}} \left(\mathrm{2}−{x}\right)^{\mathrm{4}} −\mathrm{4}\left({x}+\mathrm{2}\right)^{\mathrm{3}} \left(\mathrm{2}−{x}\right)^{\mathrm{3}} \\ $$$$\frac{{dy}}{{dx}}=\mathrm{0}\:{for}\:−\mathrm{2}\:<\:{x}\:<\:\mathrm{2}\:\:\:\Rightarrow…
Question Number 161675 by cortano last updated on 21/Dec/21 $$\:\:\begin{cases}{\mathrm{2}{x}−{y}−{e}^{−{x}} =\mathrm{0}}\\{−{x}+\mathrm{2}{y}−{e}^{−{y}} =\mathrm{0}}\end{cases} \\ $$$$\:\begin{cases}{{x}=?}\\{{y}=?}\end{cases} \\ $$ Answered by mr W last updated on 21/Dec/21 $${y}=\mathrm{2}{x}−{e}^{−{x}}…
Question Number 30599 by abdo imad last updated on 23/Feb/18 $${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