Question Number 28435 by abdo imad last updated on 25/Jan/18 $${find}\:{Q}\left({x}\right)\:/\:{nx}^{{n}+\mathrm{1}} −\left({n}+\mathrm{1}\right){x}^{{n}} +\mathrm{1}\:=\left({x}−\mathrm{1}\right)^{\mathrm{2}} {Q}\left({x}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28434 by abdo imad last updated on 25/Jan/18 $${let}\:{give}\:{the}\:{polynomial}\:{p}\left({x}\right)=\left({x}+\mathrm{1}\right)^{{n}} −\left({x}−\mathrm{1}\right)^{{n}} {with}\:{n} \\ $$$${from}\:{N}^{\ast} \\ $$$$\left.\mathrm{1}\right)\:{give}\:{the}\:{factorisation}\:{of}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} {cotan}\left(\frac{{k}\pi}{\mathrm{2}{p}+\mathrm{1}}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}{p}+\mathrm{1}}} \\ $$ Terms of…
Question Number 28432 by abdo imad last updated on 25/Jan/18 $${let}\:{put}\:{w}={e}^{{i}\frac{\mathrm{2}\pi}{{n}}} \:{calculate}\:\:{S}_{{n}} =\:\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\:\frac{\mathrm{1}}{{x}−{w}^{{k}} }\:\:{and} \\ $$$${W}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\frac{\mathrm{1}}{\left({x}−{w}^{{k}} \right)^{\mathrm{2}} }\:. \\ $$…
Question Number 28433 by abdo imad last updated on 25/Jan/18 $${let}\:{give}\:{T}_{{n}} \left({x}\right)=\:{cos}\left({narcosx}\right)\:\:{decompose}\:\frac{\mathrm{1}}{{T}_{{n}} \left({x}\right)}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 159493 by HongKing last updated on 17/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 93963 by M±th+et+s last updated on 16/May/20 $${we}\:{have}\:{for}\:{quadratic}\:{equations} \\ $$$${x}=\frac{−{b}\pm\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}{a}} \\ $$$${what}\:{about}\:{cubic}\:{equation}\:{is}\:{there}\:{any} \\ $$$${rules}\:{or}\:{ways}\:{to}\:{solve}? \\ $$ Commented by Kunal12588 last updated on…
Question Number 159494 by HongKing last updated on 17/Nov/21 Answered by qaz last updated on 18/Nov/21 $$\left(\mathrm{1}+\mathrm{a}\right)\left(\mathrm{1}+\frac{\mathrm{b}}{\mathrm{a}}\right)\left(\mathrm{1}+\frac{\mathrm{c}}{\mathrm{b}}\right)\left(\mathrm{1}+\frac{\mathrm{81}}{\mathrm{c}}\right) \\ $$$$\geqslant\left(\mathrm{1}+\sqrt{\mathrm{a}}\centerdot\sqrt{\frac{\mathrm{b}}{\mathrm{a}}}\right)^{\mathrm{2}} \left(\mathrm{1}+\sqrt{\frac{\mathrm{c}}{\mathrm{b}}}\centerdot\sqrt{\frac{\mathrm{81}}{\mathrm{c}}}\right)^{\mathrm{2}} \\ $$$$=\left(\mathrm{1}+\sqrt{\mathrm{b}}\right)^{\mathrm{2}} \left(\mathrm{1}+\sqrt{\frac{\mathrm{81}}{\mathrm{b}}}\right)^{\mathrm{2}} \\ $$$$\geqslant\left(\mathrm{1}+\sqrt[{\mathrm{4}}]{\mathrm{b}}\centerdot\sqrt[{\mathrm{4}}]{\frac{\mathrm{81}}{\mathrm{b}}}\right)^{\mathrm{4}}…
Question Number 159488 by Tawa11 last updated on 17/Nov/21 Answered by mr W last updated on 17/Nov/21 $${T}_{{n}} =\mathrm{4}{T}_{{n}−\mathrm{1}} −\mathrm{3} \\ $$$${let}\:{T}_{{n}} ={S}_{{n}} +{A} \\…
Question Number 159490 by akolade last updated on 17/Nov/21 Commented by Rasheed.Sindhi last updated on 18/Nov/21 $${Why}\:{not}\:{in}\:{one}\:{line}? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 159477 by HongKing last updated on 17/Nov/21 $$\mathrm{Find}:\:\:\:\Omega\:=\int\:\frac{\mathrm{1}}{\left(\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Answered by MJS_new last updated on 17/Nov/21 $${t}=\mathrm{arctan}\:{x} \\ $$$$\Rightarrow \\ $$$$\int\mathrm{sin}^{\mathrm{2}}…