Question Number 135108 by bramlexs22 last updated on 10/Mar/21 $$\left(\sqrt{\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}}}\:\right)^{\mathrm{x}^{\mathrm{2}} } \:=\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}+\mathrm{1}} \\ $$ Answered by MJS_new last updated on 10/Mar/21 $${x}^{\mathrm{2}} ={x}+\mathrm{1}\:\Leftrightarrow\:\frac{{x}−\mathrm{1}}{{x}}=\frac{\mathrm{1}}{{x}^{\mathrm{2}} } \\…
Question Number 4037 by Filup last updated on 27/Dec/15 $$\exists{x}\in\mathbb{Z}\exists{n}\in\mathbb{R}:{n}^{{x}} =\mathrm{2}{n} \\ $$$$\mathrm{Does}\:{x}\:{exist}? \\ $$ Commented by Filup last updated on 27/Dec/15 $${n}={x}=\mathrm{2} \\ $$$$\Rightarrow\mathrm{2}^{\mathrm{2}}…
Question Number 4036 by Rasheed Soomro last updated on 27/Dec/15 $$\mathrm{Twin}\:\mathrm{of}\:\mathrm{Q}#\mathrm{3943} \\ $$$$\mathrm{Three}\:\mathrm{circles}\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{in}\:\mathrm{a}\:\mathrm{plane} \\ $$$$\mathrm{in}\:\mathrm{such}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{a}\:\mathrm{closed}\:\mathrm{region} \\ $$$$\mathrm{is}\:\mathrm{produced}\:\mathrm{which}\:\mathrm{is}\:\mathrm{not}\:\mathrm{included} \\ $$$$\mathrm{in}\:\mathrm{any}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circles}.\:\mathrm{Determine}\:\mathrm{the} \\ $$$$\mathrm{area}\:\mathrm{of}\:\mathrm{this}\:\mathrm{region}. \\ $$$$\underset{−} {\mathrm{Circles}\:\mid\:\mathrm{Radii}\:\mid\:\mathrm{Centers}\:} \\…
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Question Number 4013 by Yozzii last updated on 26/Dec/15 $${Find}\:{x}\:{such}\:{that}\:\left({x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{5}\right)^{{x}^{\mathrm{2}} −\mathrm{21}{x}+\mathrm{10}} =\mathrm{1}. \\ $$ Commented by 123456 last updated on 26/Dec/15 $${x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{5}=\mathrm{1}\Leftrightarrow{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{4}=\mathrm{0}…
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Question Number 69538 by mind is power last updated on 24/Sep/19 $${Hello}\:{Verry}\:{Nice}\:{Day}\:{for}\:\:{You} \\ $$$${Find}\:\underset{{k}\geqslant\mathrm{0}} {\sum}\frac{\mathrm{1}}{\left(\mathrm{8}{k}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 3996 by Rasheed Soomro last updated on 26/Dec/15 $${I}\:{want}\:{to}\:{make}\:{cyllinders}\:{of}\:\boldsymbol{{maximum}} \\ $$$$\boldsymbol{{volume}}\:\boldsymbol{\mathrm{V}}_{\boldsymbol{\mathrm{max}}} \:{with}\:{minimum}\:\boldsymbol{{surface}}\:\boldsymbol{{area}}\: \\ $$$$\boldsymbol{\mathrm{S}}_{\boldsymbol{\mathrm{min}}} \:,{because}\:{they}\:{are}\:{more}\:{profitable}\:{for}\:{me}. \\ $$$${I}\:{need}\:{the}\:{help}\:{of}\:{mathematicians}\:{of}\:{this} \\ $$$${forum}. \\ $$$$ \\ $$…
Question Number 3994 by Filup last updated on 26/Dec/15 $$\mathcal{A}\mathrm{re}\:\mathrm{there}\:\mathrm{more}\:\:\mathcal{T}{rancendental} \\ $$$${or}\:\mathcal{N}{on}-\mathcal{T}{rancendental}\:{numbers}? \\ $$$$ \\ $$$$\mathcal{NOTE}: \\ $$$$\mathcal{T}{rancendentals}\:{are}\:{numbers}\:{that} \\ $$$${cannot}\:{be}\:{written}\:{algerbraically}. \\ $$$$ \\ $$$${e}.{g}.\:{x}^{\mathrm{2}} =\mathrm{2}…
Question Number 135060 by liberty last updated on 09/Mar/21