Question Number 203570 by Frix last updated on 22/Jan/24 $$\mathrm{Suggested}\:\mathrm{solution}\:\mathrm{method}\:\mathrm{to} \\ $$$$\mathrm{question}\:\mathrm{203502} \\ $$$$ \\ $$$${z}\mathrm{e}^{{z}} =\mathrm{1} \\ $$$$\mathrm{Obviously}\:\mathrm{the}\:\mathrm{only}\:\mathrm{real}\:\mathrm{solution}\:\mathrm{is} \\ $$$${z}={W}\left(\mathrm{1}\right)\approx.\mathrm{567143290} \\ $$$$ \\ $$$${z}={a}+{b}\mathrm{i}\wedge{b}\neq\mathrm{0}…
Question Number 203474 by ajfour last updated on 20/Jan/24 $$\frac{{z}^{\mathrm{4}} +\mathrm{4}{z}^{\mathrm{3}} −\mathrm{6}{z}^{\mathrm{2}} −\mathrm{4}{z}+\mathrm{1}}{{z}^{\mathrm{4}} −\mathrm{4}{z}^{\mathrm{3}} −\mathrm{6}{z}^{\mathrm{2}} +\mathrm{4}{z}+\mathrm{1}}=\frac{{z}+\mathrm{1}}{{z}−\mathrm{1}} \\ $$$${Find}\:{z}\in\mathbb{R}. \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 203502 by Frix last updated on 20/Jan/24 $${z}\mathrm{e}^{{z}} =\mathrm{e} \\ $$$$\mathrm{Obviously}\:{z}=\mathrm{1} \\ $$$$\mathrm{Now}\:\mathrm{find}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{solution}\:\mathrm{for}\:{z}\in\mathbb{C} \\ $$ Commented by Frix last updated on 22/Jan/24 $$\mathrm{See}\:\mathrm{question}\:\mathrm{203570}…
Question Number 203497 by ajfour last updated on 20/Jan/24 $${x}^{\mathrm{4}} +{cx}+{d}=\mathrm{0} \\ $$$${then}\:\:{find}\:{p}\:\:{from} \\ $$$${p}^{\mathrm{6}} −\mathrm{4}\left(\frac{{d}^{\:\mathrm{3}} }{{c}^{\mathrm{4}} }\right)^{\mathrm{1}/\mathrm{3}} {p}^{\mathrm{2}} −\mathrm{1}=\mathrm{0} \\ $$$${x}=\frac{{c}^{\mathrm{1}/\mathrm{3}} }{\mathrm{2}}\left({p}\pm\sqrt{−{p}^{\mathrm{2}} −\frac{\mathrm{8}}{{p}}}\:\right) \\…
Question Number 203448 by hardmath last updated on 19/Jan/24 $$\mathrm{y}\:=\:\mathrm{sin3x}−\mathrm{ln}\left(\mathrm{3x}+\mathrm{1}\right)+\mathrm{3}^{\mathrm{2}\boldsymbol{\mathrm{x}}} \\ $$$$\mathrm{find}:\:\:\:\mathrm{y}^{'} \:=\:? \\ $$ Commented by hardmath last updated on 19/Jan/24 $$ \\ $$find…
Question Number 203445 by mathlove last updated on 19/Jan/24 Commented by mr W last updated on 19/Jan/24 $$\Rightarrow{Q}\mathrm{203387} \\ $$ Terms of Service Privacy Policy…
Question Number 203416 by Spillover last updated on 18/Jan/24 Answered by a.lgnaoui last updated on 19/Jan/24 $$\:\: \\ $$$$\:\:\:\boldsymbol{\mathrm{R}}=\mathrm{2}\boldsymbol{\mathrm{r}}+\boldsymbol{\mathrm{BM}}\mathrm{cos}\:\boldsymbol{\alpha}\:\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\:\:\:\:\boldsymbol{\mathrm{BM}}\mathrm{sin}\:\boldsymbol{\alpha}=\boldsymbol{\mathrm{r}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{2}\right) \\ $$$$\: \\ $$$$\Rightarrow\:\:\begin{cases}{\mathrm{cos}\:\boldsymbol{\alpha}=\frac{\boldsymbol{\mathrm{R}}−\mathrm{2}\boldsymbol{\mathrm{r}}}{\boldsymbol{\mathrm{BM}}}}\\{\mathrm{sin}\:\boldsymbol{\alpha}=\frac{\boldsymbol{\mathrm{r}}}{\:\boldsymbol{\mathrm{BM}}}}\end{cases}…
Question Number 203417 by hardmath last updated on 18/Jan/24 $$\mathrm{If} \\ $$$$\mid\overline {−\mathrm{z}\:+\:\boldsymbol{\mathrm{i}}\mathrm{z}}\mid\:=\:\mathrm{2}\:\sqrt{\mathrm{13}}\:\:\:\mathrm{and}\:\:\:\mathrm{z}\:=\:\mathrm{1}\:+\:\left(\mathrm{x}\:+\:\mathrm{1}\right)\centerdot\boldsymbol{\mathrm{i}} \\ $$$$ \\ $$$$\mathrm{Find}:\:\:\:\mathrm{mun}\left(\mathrm{x}\right)\:=\:? \\ $$ Commented by hardmath last updated on…
Question Number 203378 by Calculusboy last updated on 18/Jan/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203379 by York12 last updated on 18/Jan/24 $$\mathrm{If}\:{a},{b},{c}\:\in\mathbb{R}^{+} \:\mathrm{with}\:{a}+{b}+{c}=\mathrm{3}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}^{\mathrm{6}} +{b}^{\mathrm{6}} +\mathrm{3}{c}^{\mathrm{3}} +\mathrm{4}}+\frac{\mathrm{1}}{{b}^{\mathrm{6}} +{c}^{\mathrm{6}} +\mathrm{3}{a}^{\mathrm{3}} +\mathrm{4}}+\frac{\mathrm{1}}{{c}^{\mathrm{6}} +{a}^{\mathrm{6}} +\mathrm{3}{b}^{\mathrm{3}} +\mathrm{4}}\leqslant\frac{\mathrm{3}}{\mathrm{3}+\mathrm{2}\left(\sqrt{{ab}}+\sqrt{{bc}}+\sqrt{{ac}}\right)} \\ $$ Terms…