Question Number 193195 by qaz last updated on 07/Jun/23 $$\left(−\mathrm{3}\right)^{\mathrm{666}} {mod}\mathrm{1000}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 193221 by York12 last updated on 07/Jun/23 $$ \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{cube}}\:\boldsymbol{{root}}\:\boldsymbol{{of}} \\ $$$$\mathrm{9}\boldsymbol{{ab}}^{\mathrm{2}} \:+\:\left(\boldsymbol{{b}}^{\mathrm{2}} +\mathrm{24}\boldsymbol{{a}}^{\mathrm{2}} \right)\sqrt{\boldsymbol{{b}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{{a}}^{\mathrm{2}} } \\ $$ Answered by som(math1967) last…
Question Number 193182 by York12 last updated on 06/Jun/23 $$ \\ $$$$\frac{{x}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} }+\frac{{z}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{5}^{\mathrm{2}} }+\frac{{w}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }=\mathrm{1} \\…
Question Number 193130 by Frix last updated on 04/Jun/23 $$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$${x}^{\mathrm{2}} −{c}=\sqrt{{c}−{x}} \\ $$ Commented by aba last updated on 04/Jun/23 $$\mathrm{t}=\mathrm{c}−\mathrm{x}\geqslant\mathrm{0}\: \\ $$$$\mathrm{x}^{\mathrm{2}}…
Question Number 131064 by shaker last updated on 01/Feb/21 Answered by Dwaipayan Shikari last updated on 01/Feb/21 $$\frac{\mathrm{1}}{\mathrm{4}}\int\frac{\mathrm{1}}{{x}}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }−\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{4}}\right){dx} \\ $$$$=−\frac{\mathrm{1}}{\mathrm{8}{x}^{\mathrm{2}} }−\frac{\mathrm{1}}{\mathrm{16}}\int\frac{\mathrm{1}}{{x}}−\frac{{x}}{{x}^{\mathrm{2}} +\mathrm{4}}{dx} \\…
Question Number 65495 by behi83417@gmail.com last updated on 30/Jul/19 $$\begin{cases}{\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}}+\frac{\boldsymbol{\mathrm{b}}}{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}}=\sqrt{\mathrm{3}}}\\{\frac{\boldsymbol{\mathrm{b}}}{\boldsymbol{\mathrm{a}}}+\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}}=\sqrt{\mathrm{2}}}\end{cases}\:\:\:\left[\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\boldsymbol{\mathrm{R}}\right] \\ $$ Answered by MJS last updated on 31/Jul/19 $${b}={at} \\ $$$$\begin{cases}{\frac{{t}^{\mathrm{2}} +{t}+\mathrm{1}}{{t}\left({t}+\mathrm{1}\right)}=\sqrt{\mathrm{3}}}\\{\frac{{t}^{\mathrm{2}} +{t}+\mathrm{1}}{{t}+\mathrm{1}}=\sqrt{\mathrm{2}}}\end{cases} \\…
Question Number 65480 by ajfour last updated on 30/Jul/19 $${x}^{\mathrm{4}} −\mathrm{15}{x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{24}=\mathrm{0}\:\:\: \\ $$$${solve}\:{for}\:{x}. \\ $$ Commented by Prithwish sen last updated on 30/Jul/19 $$\mathrm{x}^{\mathrm{3}}…
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Question Number 65463 by aliesam last updated on 30/Jul/19 Answered by MJS last updated on 31/Jul/19 $$\mathrm{i}^{{an}} =\mathrm{cos}\:\frac{{an}\pi}{\mathrm{2}}\:+\mathrm{i}\:\mathrm{sin}\:\frac{{an}\pi}{\mathrm{2}} \\ $$$$\mathrm{imag}\:\left(\mathrm{i}^{{n}} +\mathrm{i}^{\mathrm{2}{n}} +\mathrm{i}^{\mathrm{3}{n}} \right)\:=\mathrm{0} \\ $$$$\mathrm{sin}\:\frac{{n}\pi}{\mathrm{2}}\:+\mathrm{sin}\:{n}\pi\:+\mathrm{sin}\:\frac{\mathrm{3}{n}\pi}{\mathrm{2}}\:=\mathrm{0}…
Question Number 65457 by behi83417@gmail.com last updated on 30/Jul/19 $$\begin{cases}{\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}}+\frac{\boldsymbol{\mathrm{b}}−\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{a}}}=\mathrm{2}\sqrt{\mathrm{3}}}\\{\frac{\boldsymbol{\mathrm{b}}}{\boldsymbol{\mathrm{a}}}+\frac{\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}−\boldsymbol{\mathrm{a}}}=\mathrm{3}\sqrt{\mathrm{2}}}\end{cases}\:\:\:\:\:\left[\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\boldsymbol{\mathrm{R}},\boldsymbol{\mathrm{a}}\neq\boldsymbol{\mathrm{b}}\right] \\ $$ Answered by mr W last updated on 30/Jul/19 $${let}\:{t}=\frac{{a}}{{b}} \\ $$$${eqn}.\:\mathrm{1}\:\Rightarrow{t}+\frac{\mathrm{1}−{t}}{\mathrm{1}+{t}}=\mathrm{2}\sqrt{\mathrm{3}}\:\:\:\:\:\:…\left({i}\right) \\ $$$${eqn}.\:\mathrm{2}\:\Rightarrow\frac{\mathrm{1}}{{t}}+\frac{\mathrm{1}+{t}}{\mathrm{1}−{t}}=\mathrm{3}\sqrt{\mathrm{2}}\:\:\:\:…\left({ii}\right)…