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Question Number 58754 by azizullah last updated on 29/Apr/19 Answered by Rasheed.Sindhi last updated on 29/Apr/19 $$−{x}^{\mathrm{3}} +{x}^{\mathrm{2}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}=\mathrm{0} \\ $$$$−{x}^{\mathrm{2}} \left({x}−\mathrm{1}\right)−\mathrm{2}\left({x}^{\mathrm{2}} −\mathrm{1}\right)=\mathrm{0} \\…
Question Number 189815 by sonukgindia last updated on 22/Mar/23 Answered by Frix last updated on 22/Mar/23 $${z}=\mathrm{e}^{\mathrm{i}\theta} =\mathrm{cos}\:\theta\:+\mathrm{i}\:\mathrm{sin}\:\theta\:={c}+{s}\mathrm{i}\:\left[\mathrm{for}\:\mathrm{typing}\:\mathrm{less}\right] \\ $$$${z}^{{z}} =\left(\mathrm{e}^{\mathrm{i}\theta} \right)^{{c}+{s}\mathrm{i}} =\mathrm{e}^{−\theta{s}+\mathrm{i}\theta{c}} =\frac{\mathrm{1}}{\mathrm{e}^{\theta{s}} }\mathrm{e}^{\mathrm{i}\theta{c}}…
Question Number 124277 by SOMEDAVONG last updated on 02/Dec/20 $$\mathrm{I}.\int\frac{\mathrm{4x}^{\mathrm{2}} \mathrm{lnx}}{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\mathrm{dx}=?? \\ $$ Commented by MJS_new last updated on 02/Dec/20 $$\frac{\mathrm{4}{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} +\mathrm{1}}=\frac{\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\left(\mathrm{1}−\mathrm{i}\right)}{{x}−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\left(\mathrm{1}+\mathrm{i}\right)}+\frac{\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\left(\mathrm{1}+\mathrm{i}\right)}{{x}−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\left(\mathrm{1}−\mathrm{i}\right)}−\frac{\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\left(\mathrm{1}+\mathrm{i}\right)}{{x}+\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\left(\mathrm{1}−\mathrm{i}\right)}−\frac{\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\left(\mathrm{1}−\mathrm{i}\right)}{{x}+\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\left(\mathrm{1}+\mathrm{i}\right)} \\…
Question Number 124264 by joki last updated on 02/Dec/20 Commented by bramlexs22 last updated on 02/Dec/20 $$=−\int\:\frac{{d}\left(\mathrm{cos}\:{x}\right)}{\mathrm{cos}\:{x}}\:=\:−\ell{n}\mid\mathrm{cos}\:{x}\:\mid\:+\:{c} \\ $$$$\:=\:\ell{n}\:\mid\:\mathrm{sec}\:{x}\:\mid\:+\:{c}\: \\ $$ Commented by joki last…
Question Number 124255 by Khalmohmmad last updated on 02/Dec/20 Commented by Dwaipayan Shikari last updated on 02/Dec/20 $${One}\:{solution}\:{by}\:{observing} \\ $$$${x}=\frac{\mathrm{3}}{\mathrm{2}},\:{y}=\frac{\mathrm{3}}{\mathrm{2}}\:,\:{z}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Commented by MJS_new…
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Question Number 124247 by ZiYangLee last updated on 02/Dec/20 Commented by ZiYangLee last updated on 02/Dec/20 $$\mathrm{8}\:\mathrm{and}\:\mathrm{9},\:\mathrm{help}\:\mathrm{sir}… \\ $$ Answered by bramlexs22 last updated on…
Question Number 189786 by sonukgindia last updated on 21/Mar/23 Answered by a.lgnaoui last updated on 22/Mar/23 $${A}\bullet{z}^{{z}} =\left({e}^{{i}\theta} \right)^{{e}^{{i}\theta} } =\left(\mathrm{cos}\:\theta+{i}\mathrm{sin}\:\theta\right)^{{z}} \\ $$$$={e}^{{z}\mathrm{lnz}} =\mathrm{e}^{\mathrm{e}^{\mathrm{i}\theta} \mathrm{ln}\left(\mathrm{e}^{\mathrm{i}\theta}…
Question Number 58700 by naka3546 last updated on 28/Apr/19 $${a},\:{b},\:{c}\:\:\in\:\:\mathbb{R}^{+} \\ $$$${Find}\:\:{triple}\:\:{of}\:\:{positive}\:\:{real}\:\:{numbers}\:\left({a},\:{b},\:{c}\right)\:\:{that}\:\:{satisfy} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{a}\lfloor{b}\rfloor\:\:=\:\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{b}\lfloor{c}\rfloor\:\:=\:\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{c}\lfloor{a}\rfloor\:\:=\:\:\mathrm{12} \\ $$ Commented by Rasheed.Sindhi last updated…