Question Number 173240 by mnjuly1970 last updated on 08/Jul/22 Commented by a.lgnaoui last updated on 09/Jul/22 Commented by a.lgnaoui last updated on 09/Jul/22 $${m}+{n}=\frac{{i}}{\mathrm{2}}−\mathrm{1}\:\:\:{and}\:\:\:\:−\:\frac{{i}}{\mathrm{2}}−{i} \\…
Question Number 173242 by AgniMath last updated on 08/Jul/22 Commented by som(math1967) last updated on 09/Jul/22 $$\mathrm{2}\:\:\:\:\:\:\:\:\:\:\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}}\in\boldsymbol{{R}} \\ $$ Answered by AgniMath last updated on…
Question Number 173228 by mathlove last updated on 08/Jul/22 Answered by Frix last updated on 08/Jul/22 $$\mathrm{let}\:\mathrm{sin}\:\frac{\pi}{\mathrm{11}}\:={s}\:\wedge\:\mathrm{cos}\:\frac{\pi}{\mathrm{11}}\:={c} \\ $$$$\left(\mathrm{1}\right)\:\Rightarrow\:{y}={s}^{\mathrm{2}} {x}−\frac{{s}^{\mathrm{4}} }{\mathrm{4}} \\ $$$$\left(\mathrm{2}\right)\:\Rightarrow\:{y}=\frac{{x}}{{c}^{\mathrm{2}} }+\frac{{c}^{\mathrm{2}} }{\mathrm{4}}…
Question Number 173224 by cortano1 last updated on 08/Jul/22 Answered by Frix last updated on 08/Jul/22 $${x}=\mathrm{6} \\ $$ Commented by Michaelfaraday last updated on…
Question Number 107690 by bemath last updated on 12/Aug/20 $$\:\:\:\:\:\:\:\:“\mathcal{B}{e}\mathcal{M}{ath}“ \\ $$$${Let}\:{the}\:{complex}\:{number}\:{z}\:{satisfies}\:{the} \\ $$$${equation}\:\mathrm{3}\left({z}−\mathrm{1}\right)=\:{i}\left({z}+\mathrm{1}\right)\: \\ $$$$\left(\mathrm{1}\right)\:{find}\:{z}\:{in}\:{the}\:{form}\:{a}+{bi}\:{where}\:{a},{b}\:\in\mathbb{R}\: \\ $$$$\left(\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\mid{z}\mid\:{and}\:\mid{z}−{z}^{\ast} \mid\: \\ $$$$ \\ $$ Answered by…
Question Number 173226 by AgniMath last updated on 08/Jul/22 $$\:\:\:\:\boldsymbol{\mathrm{Factorize}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\:\frac{\mathrm{1}}{\mathrm{4}}\:\left({a}\:+\:{b}\right)^{\mathrm{2}} \:−\:\frac{\mathrm{9}}{\mathrm{16}}\:\left(\mathrm{2}{a}\:−\:{b}\right)^{\mathrm{2}} \\ $$ Commented by mr W last updated on 08/Jul/22 $$=\left(\frac{{a}+{b}}{\mathrm{2}}\right)^{\mathrm{2}} −\left[\frac{\mathrm{3}\left(\mathrm{2}{a}−{b}\right)}{\mathrm{4}}\right]^{\mathrm{2}}…
Question Number 173227 by mnjuly1970 last updated on 08/Jul/22 Commented by mr W last updated on 08/Jul/22 $${not}\:\mathrm{1234567900}? \\ $$ Answered by floor(10²Eta[1]) last updated…
Question Number 173216 by Shrinava last updated on 08/Jul/22 $$\mathrm{O}-\mathrm{circumcenter}\:,\:\mathrm{I}-\mathrm{incenter},\:\mathrm{R}-\mathrm{circumradii}, \\ $$$$\mathrm{r}-\mathrm{radii},\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}-\mathrm{sides}\:\mathrm{in}\:\mathrm{a}\:\mathrm{bicenteric} \\ $$$$\mathrm{quadrilateral}.\:\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{20I}^{\mathrm{2}} \:+\:\mathrm{r}\:\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\sqrt{\mathrm{4R}^{\mathrm{2}} \:−\:\mathrm{a}^{\mathrm{2}} }\:=\:\mathrm{2}\left(\mathrm{R}^{\mathrm{2}} \:+\:\mathrm{2r}^{\mathrm{2}} \right) \\ $$ Terms…
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Question Number 173212 by peter frank last updated on 08/Jul/22 Answered by Frix last updated on 08/Jul/22 $$\mathrm{3}{x}^{\mathrm{3}} −\mathrm{2}{x}−\mathrm{6}=\mathrm{3}\left({x}−{r}\right)\left({x}^{\mathrm{2}} +{rx}+{s}\right) \\ $$$$\mathrm{there}'\mathrm{s}\:\mathrm{no}\:\mathrm{useable}\:\mathrm{solution} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}\int\frac{{dx}}{\left({x}−{r}\right)\left({x}^{\mathrm{2}} +{rx}+{s}\right)}=…