Question Number 45527 by Sanjarbek last updated on 14/Oct/18 Commented by Meritguide1234 last updated on 14/Oct/18 Commented by maxmathsup by imad last updated on 14/Oct/18…
Question Number 176595 by MASANJAJJ last updated on 22/Sep/22 Answered by Rasheed.Sindhi last updated on 22/Sep/22 $$\left.\mathrm{b}\right) \\ $$$$\:\:\:\left(\mathrm{2}{k}\right)^{\mathrm{2}} +\left(\mathrm{2}{k}+\mathrm{2}\right)^{\mathrm{2}} =\left(\mathrm{2}{k}+\mathrm{4}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\mathrm{4}{k}^{\mathrm{2}} +\mathrm{4}{k}^{\mathrm{2}} +\mathrm{8}{k}+\mathrm{4}=\mathrm{4}{k}^{\mathrm{2}}…
Question Number 111046 by Algoritm last updated on 01/Sep/20 Commented by Her_Majesty last updated on 02/Sep/20 $$\mathrm{80} \\ $$ Terms of Service Privacy Policy Contact:…
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Question Number 111044 by mathdave last updated on 01/Sep/20 Commented by kaivan.ahmadi last updated on 01/Sep/20 $$\mathrm{5}. \\ $$$${a}\mid{m},{b}\mid{m}\Rightarrow{ab}\mid{m}\:{on}\:{the}\:{other}\:{hand} \\ $$$${lcm}\left({a},{b}\right)\mid{ab}\:{so}\:{lcm}\left({a},{b}\right)\mid{m}. \\ $$$$\mathrm{6}. \\ $$$${let}\:{a},{b}\in\mathbb{R}…
Question Number 111043 by mathdave last updated on 01/Sep/20 $${solve}\:{the}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{\:\sqrt{{x}}\left(\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} \right)^{\frac{\mathrm{3}}{\mathrm{4}}} }{dx} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 45500 by Sanjarbek last updated on 13/Oct/18 Answered by MrW3 last updated on 13/Oct/18 $${x}=\mathrm{64}^{\frac{\mathrm{1}}{{x}}} ={e}^{\frac{\mathrm{ln}\:\mathrm{64}}{{x}}} \\ $$$$\mathrm{1}=\frac{\mathrm{1}}{{x}}{e}^{\frac{\mathrm{ln}\:\mathrm{64}}{{x}}} \\ $$$$\mathrm{ln}\:\mathrm{64}=\frac{\mathrm{ln}\:\mathrm{64}}{{x}}{e}^{\frac{\mathrm{ln}\:\mathrm{64}}{{x}}} \\ $$$$\frac{\mathrm{ln}\:\mathrm{64}}{{x}}=\mathbb{W}\left(\mathrm{ln}\:\mathrm{64}\right)\:\leftarrow{Lambert}\:{W}\:{function} \\…
Question Number 111039 by mathdave last updated on 01/Sep/20 $${solve}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+{x}^{\mathrm{6}} }{dx} \\ $$$${mr}\:\:{abbo}\:{your}\:{question}\: \\ $$ Answered by mathdave last updated on…
Question Number 111035 by ZiYangLee last updated on 01/Sep/20 $$\mathrm{If}\:{b}\in\mathbb{Z}^{+} \:\forall\:\mathrm{both}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{equation} \\ $$$${x}^{\mathrm{2}} −{bx}+\mathrm{132}=\mathrm{0}\:\mathrm{are}\:\mathrm{integers}. \\ $$$$\mathrm{Find} \\ $$$$\left(\mathrm{1}\right)\mathrm{the}\:\mathrm{largest}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:{b} \\ $$$$\left(\mathrm{2}\right)\mathrm{the}\:\mathrm{smallest}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:{b}. \\ $$ Answered by 1549442205PVT…