Question Number 151216 by liberty last updated on 19/Aug/21 $$\:\:\:\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{number}\: \\ $$$$\:\:\sqrt[{\mathrm{7}}]{\mathrm{x}+\mathrm{3}}\:+\sqrt[{\mathrm{7}}]{\mathrm{6}−\mathrm{x}}\:=\:\sqrt[{\mathrm{7}}]{\mathrm{9}}\: \\ $$ Answered by MJS_new last updated on 19/Aug/21 $$\mathrm{very}\:\mathrm{obviously}\:{x}=−\mathrm{3}\vee{x}=\mathrm{6} \\ $$ Commented…
Question Number 151218 by peter frank last updated on 19/Aug/21 Commented by dumitrel last updated on 19/Aug/21 $$\forall\:{w}\:????? \\ $$ Commented by dumitrel last updated…
Question Number 151212 by mathdanisur last updated on 19/Aug/21 $$\mathrm{if}\:\:\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,…\mathrm{a}_{\boldsymbol{\mathrm{n}}} >\mathrm{1}\:\:\mathrm{then}: \\ $$$$\sqrt{\frac{\left(\mathrm{a}_{\mathrm{1}} -\mathrm{1}\right)\left(\mathrm{a}_{\mathrm{2}} -\mathrm{1}\right)…\left(\mathrm{a}_{\boldsymbol{\mathrm{n}}} -\mathrm{1}\right)}{\left(\mathrm{a}_{\mathrm{1}} +\mathrm{1}\right)\left(\mathrm{a}_{\mathrm{2}} +\mathrm{1}\right)…\left(\mathrm{a}_{\boldsymbol{\mathrm{n}}} +\mathrm{1}\right)}}\:\leqslant\:\frac{\mathrm{a}_{\mathrm{1}} \mathrm{a}_{\mathrm{2}} …\mathrm{a}_{\boldsymbol{\mathrm{n}}} }{\mathrm{2}^{\boldsymbol{\mathrm{n}}} }…
Question Number 151215 by mathdanisur last updated on 19/Aug/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:;\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{1}\:\mathrm{and}\:\lambda\geqslant\frac{\mathrm{1}}{\mathrm{6}}\:\mathrm{then}: \\ $$$$\boldsymbol{\lambda}\:\Sigma\:\frac{\mathrm{y}\:+\:\mathrm{z}}{\mathrm{x}}\:+\:\mathrm{3}\:\Sigma\:\mathrm{yz}\:\geqslant\:\mathrm{6}\boldsymbol{\lambda}\:+\:\mathrm{1} \\ $$ Answered by dumitrel last updated on 19/Aug/21 $${p}=\mathrm{1} \\ $$$${p}^{\mathrm{2}} \geqslant\mathrm{3}{q}\Rightarrow{q}\leqslant\frac{\mathrm{1}}{\mathrm{3}}\leqslant\mathrm{2}\lambda…
Question Number 85676 by john santu last updated on 24/Mar/20 $$\int\underset{\mathrm{0}} {\overset{\infty} {\:}}\:\frac{{dx}}{\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} } \\ $$$${let}\:{x}\:=\:\mathrm{tan}\:{t}\:\Rightarrow{dx}=\mathrm{sec}\:^{\mathrm{2}} {t}\:{dt} \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{sec}\:^{\mathrm{2}} {t}\:{dt}}{\left(\mathrm{tan}\:{t}+\mathrm{sec}\:{t}\right)^{\mathrm{2}} }\:=\: \\…
Question Number 85677 by john santu last updated on 24/Mar/20 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{sin}\:\left(\frac{\mathrm{21}{x}}{\mathrm{2}}\right)}{\mathrm{sin}\:\left(\frac{{x}}{\mathrm{2}}\right)}\:{dx}\: \\ $$ Commented by jagoll last updated on 24/Mar/20 $$\mathrm{i}\:\mathrm{don}'\mathrm{t}\:\mathrm{have}\:\mathrm{a}\:\mathrm{simple}\:\mathrm{way}\:\mathrm{to}\:\mathrm{solve} \\ $$$$\mathrm{it}…
Question Number 151208 by liberty last updated on 19/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 20138 by tammi last updated on 22/Aug/17 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:{ax}}{\mathrm{1}−\mathrm{cos}\:{bx}} \\ $$$$ \\ $$ Answered by ajfour last updated on 22/Aug/17 $$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2sin}\:^{\mathrm{2}} \left(\frac{{ax}}{\mathrm{2}}\right)}{\mathrm{2sin}\:^{\mathrm{2}}…
Question Number 151211 by EDWIN88 last updated on 19/Aug/21 $$\:{Find}\:{the}\:{coefficient}\:{of}\:{x}^{\mathrm{9}} \: \\ $$$${from}\:{expression}\: \\ $$$$\:\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{3}{x}^{\mathrm{3}} \right)\left(\mathrm{1}+\mathrm{4}{x}^{\mathrm{4}} \right)\left(\mathrm{1}+\mathrm{5}{x}^{\mathrm{5}} \right)…\left(\mathrm{1}+\mathrm{10}{x}^{\mathrm{10}} \right) \\ $$ Answered by Olaf_Thorendsen…
Question Number 151205 by EDWIN88 last updated on 19/Aug/21 $$\underbrace{ }\:\begin{array}{|c|c|}{\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{{x}} +\mathrm{1}\:=\left(\mathrm{2}\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\right)^{{x}} }\\{{x}\:=?\:}\\\hline\end{array} \\ $$ Answered by bramlexs22 last updated on 19/Aug/21 $$\:\frac{\mathrm{1}}{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{x}} }\:+\:\mathrm{1}\:=\:\frac{\mathrm{2}^{\mathrm{x}} }{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\frac{\mathrm{x}}{\mathrm{2}}}…