Question Number 61479 by Tawa1 last updated on 03/Jun/19 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}:\:\:\:\:\:\:\:\frac{\mathrm{6}\sqrt{\mathrm{2x}}}{\mathrm{x}\:−\:\mathrm{1}}\:+\:\frac{\mathrm{5}\sqrt{\mathrm{x}\:−\:\mathrm{1}}}{\mathrm{2x}}\:\:\:=\:\:\mathrm{13} \\ $$ Commented by MJS last updated on 03/Jun/19 $$\mathrm{we}\:\mathrm{cannot}\:\mathrm{generally}\:\mathrm{solve}\:\mathrm{this}… \\ $$ Answered by ajfour…
Question Number 192420 by Mingma last updated on 17/May/23 Commented by AST last updated on 18/May/23 $${Q}\mathrm{191758} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 61313 by Tony Lin last updated on 31/May/19 $$\left.{how}\:{to}\:{calculate}\:\underset{{n}\rightarrow+\infty} {\mathrm{lim}0}.\mathrm{05}^{\mathrm{0}.\mathrm{05}^{\mathrm{0}.\mathrm{05}^{.^{.^{.\mathrm{0}.\mathrm{05}} } } } } \right\}{n} \\ $$$${in}\:{a}\:{simple}\:{and}\:{fast}\:{way}? \\ $$ Commented by mr W…
Question Number 192367 by Rupesh123 last updated on 15/May/23 Answered by mehdee42 last updated on 15/May/23 $${t}_{{r}} ={r}−\frac{\mathrm{3}}{\mathrm{2}}\Rightarrow{t}_{{r}+\mathrm{1}} ={r}−\frac{\mathrm{1}}{\mathrm{2}}\:\&\:{t}_{{r}+\mathrm{2}} ={r}+\frac{\mathrm{1}}{\mathrm{2}}\&\:{t}_{{r}+\mathrm{3}} ={r}+\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\Rightarrow{t}_{{r}} {t}_{{r}+\mathrm{1}} {t}_{{r}+\mathrm{2}}…
Question Number 126795 by mathocean1 last updated on 24/Dec/20 $${N}\:{is}\:{a}\:{number}\:\in\:\mathbb{N}\:{which}\:{has}\:{three} \\ $$$${digits}\:{and}\:{written}\:{xyz}\:{in}\:{base}\:\mathrm{10}\: \\ $$$${such}\:{that}\:\begin{cases}{{xy}+{xz}+{yz}={xyz}}\\{\mathrm{0}<{x}<{y}<{z}}\end{cases} \\ $$$${Determinate}\:{N}. \\ $$ Commented by JDamian last updated on 24/Dec/20…
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Question Number 192266 by Shlock last updated on 13/May/23 Answered by Frix last updated on 13/May/23 $$\mathrm{Since}\:{a}\in\mathbb{N}\wedge\mathrm{0}\leqslant{a}\leqslant\mathrm{9}\:\mathrm{it}'\mathrm{s}\:\mathrm{best}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{for} \\ $$$${n}\:\mathrm{and}\:\mathrm{try}: \\ $$$$\mathrm{2}{n}^{\mathrm{2}} +\mathrm{14}{n}+\mathrm{83}=\mathrm{1111}{a} \\ $$$${n}=\frac{−\mathrm{7}+\sqrt{\mathrm{2222}{a}−\mathrm{117}}}{\mathrm{2}} \\…
Question Number 192208 by Shlock last updated on 11/May/23 Answered by witcher3 last updated on 11/May/23 $$\Rightarrow\forall\left(\mathrm{7k}+\mathrm{r}\right)\in\mathbb{N}\Rightarrow\exists\left(\mathrm{a},\mathrm{b},\mathrm{c}\right)\in\left[\mathrm{7k}+\mathrm{r},\mathrm{7k}+\mathrm{r}+\mathrm{6}\right] \\ $$$$\mathrm{r}\in\left\{\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\right\} \\ $$$$\mathrm{a}\equiv\mathrm{r}+\mathrm{1}\left[\mathrm{7}\right];\mathrm{a}=\mathrm{7k}+\mathrm{r}+\mathrm{1} \\ $$$$\mathrm{b}\equiv\mathrm{r}+\mathrm{2}\left[\mathrm{7}\right];\mathrm{b}=\mathrm{7k}+\mathrm{r}+\mathrm{2} \\ $$$$\mathrm{c}\equiv\mathrm{r}+\mathrm{4}\left[\mathrm{7}\right];\mathrm{c}=\mathrm{7k}+\mathrm{r}+\mathrm{4}…
Question Number 192187 by alcohol last updated on 10/May/23 $$\begin{cases}{{z}_{\mathrm{1}} \:+\:{z}_{\mathrm{2}} \:=\:{a}}\\{{z}_{\mathrm{2}} \:+\:{z}_{\mathrm{3}} \:=\:{b}}\\{{z}_{\mathrm{3}} \:+\:{z}_{\mathrm{4}} \:=\:{c}}\\{{z}_{\mathrm{1}} \:+\:{z}_{\mathrm{4}} \:=\:{d}}\end{cases} \\ $$$${solve}\:{using}\:{gaussian}\:{elimination} \\ $$ Terms of Service…
Question Number 61096 by Arthur El-bomart last updated on 29/May/19 $$\forall\:{a},\:{n}\:\in\:{N}\::\:\mid{a}−{n}\mid=\mathrm{1}\:{pour}\:{a},\:{n}\:\geqslant\mathrm{3} \\ $$$${a}^{{m}} \equiv\mathrm{1}{modn}\:\left(\ast\right) \\ $$$${posons}\::\:{m}={n}−\mathrm{1}\:\left(\ast'\right) \\ $$$${subtituons}\:{cette}\:{valeur}\:{dans}\:\left(\ast\right). \\ $$$${on}\:{a}:\:{a}^{{n}−\mathrm{1}} \equiv\mathrm{1}{modn}.\:{Mais}\:{n}\:{n}'{est}\:{pas}\:{forcement}\:{premier}. \\ $$$${Test}\:{de}\:{primalite} \\ $$$$\forall\:{n}\:\in\:{N},\:{n}\:\geqslant\mathrm{3}.…