Question Number 16519 by tawa tawa last updated on 23/Jun/17 $$\mathrm{Solve}: \\ $$$$\mid\mathrm{2}\:−\:\mathrm{x}\mid\:−\:\mathrm{2}\:\mid\mathrm{x}\:+\:\mathrm{1}\mid\:<\:\mathrm{1} \\ $$ Answered by ajfour last updated on 23/Jun/17 Commented by ajfour…
Question Number 147587 by mathdanisur last updated on 22/Jul/21 Commented by ajfour last updated on 22/Jul/21 $${what}\:{if}\:{we}\:{replace}\:{the}\:{r}.{h}.{s}.\:{in} \\ $$$${this}\:{question}\:{by}\:\:\mathrm{2}{x}\:? \\ $$ Answered by iloveisrael last…
Question Number 147585 by mathdanisur last updated on 22/Jul/21 Answered by Rasheed.Sindhi last updated on 22/Jul/21 $$\:\:\:{z}={w}+{f}\::\:{whole}\:{number}\:\&\:{fraction}<\mathrm{1} \\ $$$$\:\:\:\:{w}+{f}−\mathrm{2021}{f}=\mathrm{2021} \\ $$$$\:\:\:\:{w}=\mathrm{2021}{f}−{f}+\mathrm{2021} \\ $$$$\:\:\:\:{w}=\mathrm{2020}{f}+\mathrm{2021} \\ $$$${Let}\:{f}=\frac{{p}}{{q}}\:;\:{p}\:\&\:{q}\:{coprime}\:{p}<{q}…
Question Number 147582 by mathdanisur last updated on 22/Jul/21 $${if}\:\:{x};{y};{z}>\mathrm{0}\:\:{prove}\:{that} \\ $$$$\frac{{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} }{{xyz}}\:\geqslant\:\mathrm{2}\left(\frac{{x}}{{y}+{z}}\:+\:\frac{{y}}{{z}+{x}}\:+\:\frac{{z}}{{x}+{y}}\right) \\ $$ Answered by mitica last updated on 22/Jul/21 $${m}_{{h}}…
Question Number 82041 by M±th+et£s last updated on 17/Feb/20 $${show}\:{that} \\ $$$$\pi^{{ie}} +\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{0} \\ $$ Commented by mr W last updated on 17/Feb/20 $${certainly}\:{it}'{s}\:{not}\:{your}\:{fault}\:{that}\:{it}\:{is} \\…
Question Number 147572 by liberty last updated on 22/Jul/21 $$\:\:\:\underset{{n}\geqslant\mathrm{1}} {\sum}\:\frac{\mathrm{4}{n}−\mathrm{3}}{\left({n}^{\mathrm{2}} +\mathrm{2}{n}\right)\left({n}+\mathrm{3}\right)}\:=? \\ $$ Answered by mathmax by abdo last updated on 22/Jul/21 $$\mathrm{let}\:\mathrm{S}=\sum_{\mathrm{n}=\mathrm{1}} ^{\infty}…
Question Number 147566 by mathdanisur last updated on 21/Jul/21 $${x}^{\mathrm{3}} \:+\:\mathrm{3367}\:=\:\mathrm{2}^{\boldsymbol{{n}}} \:\:\Rightarrow\:{x}\:;\:{n}\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 21/Jul/21 $${x}^{\mathrm{3}} +\mathrm{3367}\:=\:\mathrm{2}^{{n}} \\ $$$$\mathrm{Solution}\:\mathrm{for}\:{x}\in\mathbb{N}.…
Question Number 82031 by M±th+et£s last updated on 17/Feb/20 $${find}\:{x},{y} \\ $$$$\begin{cases}{\mathrm{5}\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{y}^{\mathrm{4}} }\:=\mathrm{4}{x}−\mathrm{3}{y}}\\{\mathrm{4}\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{y}^{\mathrm{4}} }\:=\mathrm{3}{x}−\mathrm{2}{y}}\end{cases} \\ $$ Answered by MJS last updated on 17/Feb/20…
Question Number 147557 by mathdanisur last updated on 21/Jul/21 $${Simlify} \\ $$$$\left(\frac{\mathrm{1}+\sqrt{{x}}}{\:\sqrt{\mathrm{1}+{x}}}\:−\:\frac{\sqrt{\mathrm{1}+{x}}}{\mathrm{1}+\sqrt{{x}}}\right)^{\mathrm{2}} -\:\left(\frac{\mathrm{1}−\sqrt{{x}}}{\:\sqrt{\mathrm{1}+{x}}}\:−\:\frac{\sqrt{\mathrm{1}+{x}}}{\mathrm{1}−\sqrt{{x}}}\right)^{\mathrm{2}} \\ $$ Answered by Rasheed.Sindhi last updated on 21/Jul/21 $$\left(\underset{{a}} {\underbrace{\frac{\mathrm{1}+\sqrt{{x}}}{\:\sqrt{\mathrm{1}+{x}}}\:}}−\:\frac{\sqrt{\mathrm{1}+{x}}}{\mathrm{1}+\sqrt{{x}}}\right)^{\mathrm{2}} -\:\left(\underset{{b}}…
Question Number 147553 by Ar Brandon last updated on 21/Jul/21 Answered by ArielVyny last updated on 22/Jul/21 $$\left.\mathrm{1}\right){Formule}\:{de}\:{Poincarre}\:{se}\:{demontre}\:{par}\: \\ $$$${reccurence} \\ $$$$\left.\mathrm{2}\right){soit}\:{f}\:\:{l}'{application}\:{qui}\:{a}\:{une}\:{lettre}\:{i}\:{on}\: \\ $$$${associe}\:{un}\:{destinataire}\:{ou}\:{f}\left({i}\right)\:{est}\:{la}\:{lettre} \\…