Question Number 70838 by A8;15: last updated on 08/Oct/19 Answered by mind is power last updated on 08/Oct/19 $${X}^{\mathrm{3}} −\mathrm{1}=\left({X}−\mathrm{1}\right)\left({X}^{\mathrm{2}} +{X}+\mathrm{1}\right) \\ $$$${X}^{\mathrm{3}} +\mathrm{1}=\left({X}+\mathrm{1}\right)\left({X}^{\mathrm{2}} −{X}+\mathrm{1}\right)…
Question Number 70834 by Maclaurin Stickker last updated on 08/Oct/19 Answered by mind is power last updated on 08/Oct/19 $$\sum_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \frac{\mathrm{1}}{{log}_{{x}} \left(\mathrm{2}^{{k}} \right){log}_{{x}} \left(\mathrm{2}^{\left.{k}+\mathrm{1}\right)}…
Question Number 70826 by naka3546 last updated on 08/Oct/19 Commented by naka3546 last updated on 08/Oct/19 $${Find}\:\:{x}\:. \\ $$ Answered by mind is power last…
Question Number 136356 by SOMEDAVONG last updated on 21/Mar/21 $$\mathrm{L}=\underset{\mathrm{n}\rightarrow\propto} {\mathrm{lim}}\left[\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{n}+\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{n}+\mathrm{2}}\:+\:…+\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{n}+\mathrm{n}}\right] \\ $$ Answered by mindispower last updated on 21/Mar/21 $$\underset{{k}\leqslant{n}} {\sum}\frac{\mathrm{1}}{{n}^{\mathrm{2}}…
Question Number 136355 by mohammad17 last updated on 21/Mar/21 Answered by Dwaipayan Shikari last updated on 21/Mar/21 $${i}^{{i}} =\left({e}^{\frac{\pi{i}}{\mathrm{2}}} \right)^{{i}} ={e}^{−\frac{\pi}{\mathrm{2}}} =\Phi \\ $$$${i}^{{log}\left({i}\right)} =\left({e}^{\frac{\pi}{\mathrm{2}}{i}}…
Question Number 136344 by Gideon last updated on 21/Mar/21 Commented by mindispower last updated on 21/Mar/21 $${x}^{\mathrm{2}} +\mathrm{6}{x}=\left({x}+\mathrm{3}\right)^{\mathrm{2}} −\mathrm{9} \\ $$$${t}=\left({x}+\mathrm{3}\right)^{\mathrm{2}} \\ $$$$\frac{\mathrm{5}}{\:\sqrt{{t}−\mathrm{1}}}+\frac{\mathrm{1}}{\:\sqrt{{t}−\mathrm{4}}}=\frac{\mathrm{4}}{{t}} \\ $$$${we}\:{have}\:{t}>\mathrm{4},{t}−\mathrm{1}>\mathrm{3}\Rightarrow\sqrt{{t}−\mathrm{1}}<{t}\Leftrightarrow…
Question Number 136346 by ZiYangLee last updated on 21/Mar/21 $$\mathrm{If}\:\mathrm{1},\omega\:\mathrm{and}\:\omega^{\mathrm{2}} \:\mathrm{are}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{unity}, \\ $$$$\mathrm{prove}\:\mathrm{that}\:\left(\mathrm{1}−\omega\right)\left(\mathrm{1}−\omega^{\mathrm{2}} \right)\left(\mathrm{1}−\omega^{\mathrm{4}} \right)\left(\mathrm{1}−\omega^{\mathrm{5}} \right)=\mathrm{9} \\ $$ Answered by Rasheed.Sindhi last updated on 21/Mar/21…
Question Number 136331 by mohammad17 last updated on 20/Mar/21 Answered by mr W last updated on 20/Mar/21 $$\mathrm{5}×\mathrm{3}^{{n}+\mathrm{1}} ×\mathrm{2}^{\mathrm{1}−\mathrm{2}{n}} \\ $$$$=\mathrm{5}×\mathrm{3}^{{n}} ×\mathrm{3}×\mathrm{2}×\mathrm{4}^{−{n}} \\ $$$$=\mathrm{30}×\left(\frac{\mathrm{3}}{\mathrm{4}}\overset{{n}} {\right)}…
Question Number 70782 by oyemi kemewari last updated on 08/Oct/19 $$\mathrm{how}\:\mathrm{can}\:\mathrm{i}\:\mathrm{get}\:\mathrm{my}\:\mathrm{password}\:?\:\mathrm{i}\:\:\mathrm{can}'\mathrm{t}\:\mathrm{remeber} \\ $$ Commented by Tinku Tara last updated on 08/Oct/19 There is no option to retrieve forgotten password. Commented by oyemi…
Question Number 136320 by radians last updated on 20/Mar/21 Answered by Olaf last updated on 20/Mar/21 $$\mathrm{coefficient}\:{x}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{same}\:\mathrm{as}\:{x}^{\mathrm{3}} \:: \\ $$$$\Rightarrow\:\mathrm{C}_{\mathrm{2}} ^{\mathrm{2020}} {a}^{\mathrm{2}} {b}^{\mathrm{2018}} \:=\:\mathrm{C}_{\mathrm{3}}…