Question Number 96311 by bemath last updated on 31/May/20 $$\left(\mathrm{4}+\sqrt{\mathrm{15}}\right)^{{x}} \:+\:\left(\mathrm{4}−\sqrt{\mathrm{15}}\right)^{{x}} \:=\:\mathrm{62}\: \\ $$$${x}=? \\ $$ Answered by bobhans last updated on 31/May/20 $$\mathrm{4}−\sqrt{\mathrm{15}}\:×\:\frac{\mathrm{4}+\sqrt{\mathrm{15}}}{\mathrm{4}+\sqrt{\mathrm{15}}}\:=\:\frac{\mathrm{1}}{\mathrm{4}+\sqrt{\mathrm{15}}} \\…
Question Number 96296 by Enyz last updated on 31/May/20 Answered by Enyz last updated on 01/Jun/20 Commented by Enyz last updated on 01/Jun/20 Is this correct? Terms…
Question Number 96289 by rb222 last updated on 31/May/20 $$\mathrm{1010}^{{x}} +\mathrm{2020}^{{x}} =\mathrm{4040}^{{x}} \\ $$$${x}=? \\ $$ Commented by bobhans last updated on 31/May/20 $$\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{{x}} +\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{{x}}…
Question Number 161820 by HongKing last updated on 22/Dec/21 $$\mathrm{Solve}\:\mathrm{this}\:\mathrm{differential}\:\mathrm{equation}: \\ $$$${a}\:\frac{\partial{L}\left(\alpha\right)}{\partial{a}}\:+\:{b}\:\frac{\partial{L}\left(\alpha\right)}{\partial{b}}\:=\:{L}\left(\alpha\right) \\ $$$$\mathrm{where}:\:{L}\left(\alpha\right)\:=\:\underset{\:\mathrm{0}} {\overset{\:\boldsymbol{{a}}} {\int}}\sqrt{{a}^{\mathrm{2}} {sin}^{\mathrm{2}} \left({t}\right)\:+\:{b}^{\mathrm{2}} {cos}^{\mathrm{2}} \left({t}\right)}\:{dt} \\ $$ Answered by aleks041103…
Question Number 161822 by HongKing last updated on 22/Dec/21 $$\mathrm{Find}: \\ $$$$\Omega\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\left[\underset{\boldsymbol{\mathrm{i}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{k}}} {\sum}}\left(\mathrm{i}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\right]^{\:-\mathrm{1}} =\:? \\ $$ Answered by qaz last updated…
Question Number 161817 by HongKing last updated on 22/Dec/21 Answered by aleks041103 last updated on 23/Dec/21 $${f}\left({x}\right)=\left({e}^{−\mathrm{1}} \circ{g}\circ{e}\right)\left({x}\right) \\ $$$${e}\left({x}\right)={x}^{\mathrm{2021}} \\ $$$${g}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}−{x}} \\ $$$${e}^{−\mathrm{1}} \left({x}\right)={x}^{\mathrm{1}/\mathrm{2021}}…
Question Number 161818 by HongKing last updated on 22/Dec/21 $$\mathrm{Show}\:\mathrm{that}: \\ $$$$\Phi\:=\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\sqrt{\frac{\mathrm{1}\:-\:\mathrm{x}^{\mathrm{2}} }{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:=\:\frac{\sqrt{\pi}}{\mathrm{4}}\:\left(\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\Gamma\left(\frac{\mathrm{3}}{\mathrm{4}}\right)}\:-\:\mathrm{4}\:\frac{\Gamma\left(\frac{\mathrm{3}}{\mathrm{4}}\right)}{\Gamma\left(\frac{\mathrm{1}}{\mathrm{4}}\right)}\right) \\ $$$$\mathrm{where}:\:\Gamma-\mathrm{Gamma}\:\mathrm{function} \\ $$ Answered by Lordose last updated…
Question Number 30745 by abdo imad last updated on 25/Feb/18 $${let}\:\:{U}_{{n}} =\left\{{z}\in{C}/{z}^{{n}} =\mathrm{1}\right\}\:\:{simlify} \\ $$$${A}_{{n}} =\:\sum_{\alpha\in{U}_{{n}} } \:\left({x}+\alpha\right)^{{n}} \:{and}\:{B}_{{n}} =\sum_{\alpha\in\:{U}_{{n}} } \:\:\left({x}−\alpha\right)^{{n}} . \\ $$…
Question Number 30743 by abdo imad last updated on 25/Feb/18 $${decompose}\:{inside}\:{R}\left[{x}\right]\:\:{p}\left({x}\right)={x}^{\mathrm{2}{n}+\mathrm{1}} \:−\mathrm{1}\:{then}\:{find} \\ $$$$\prod_{{k}=\mathrm{1}} ^{{n}} \:{sin}\left(\:\frac{{k}\pi}{\mathrm{2}{n}+\mathrm{1}}\right)\:. \\ $$ Commented by abdo imad last updated on…
Question Number 30744 by abdo imad last updated on 25/Feb/18 $${let}\:{p}\left({x}\right)=\:\left({x}−\mathrm{1}\right)^{{n}} \:−{x}^{{n}} \:+\mathrm{1}\:\:{with}\:{n}\:{integr}\:{find}\:{n} \\ $$$${in}\:{ordre}\:{that}\:{p}\left({x}\right)\:{have}\:{a}\:{double}\:{root}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com