Category: Arithmetic

Question Number 189970 by Rupesh123 last updated on 25/Mar/23 Answered by Rasheed.Sindhi last updated on 25/Mar/23 $$x,y,x+y,x-y\in \mathbb{P};x,y=?$$$$\bullet Ifxandywerebothoddprimes$$$$\Rightarrow 2\mid (x+y)\Rightarrow x+y\notin \mathbb{P}orx+y=2$$$$x+y=2hasnosolutioninprime$$$$\bullet{If}\:{x}={y}=\mathrm{2}\Rightarrow\:{x}+{y},{x}−{y}\:\notin\mathbb{P}…

Question Number 58804 by Tawa1 last updated on 30/Apr/19 $$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x}:4\cos \mathrm{x}+3\sin \mathrm{x}=2$$ Commented by MJS last updated on 30/Apr/19 $$\mathrm{generally}$$$$a\cos x+b\sin x=c$$$${x}=\mathrm{2arctan}\:{t} \…

Question Number 124116 by danielasebhofoh last updated on 30/Nov/20 Answered by Dwaipayan Shikari last updated on 01/Dec/20 $$\int x^{-x}dx$$$$=\underset{{n}\geqslant\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \int\frac{\left({xlogx}\right)^{{n}} }{{n}!}{dx}…

Question Number 189624 by Rupesh123 last updated on 19/Mar/23 Answered by Rasheed.Sindhi last updated on 19/Mar/23 $$x^2-(a+b)x+ab=x^2+(c-6)x-6c+5$$$$-(a+b)=c-6\wedge ab=5-6c$$$$c=-a-b+6\wedge ab=5-6(-a-b+6)$$$${ab}=\mathrm{6}{a}+\mathrm{6}{b}−\mathrm{31}…

Question Number 189563 by Rupesh123 last updated on 18/Mar/23 Answered by FelipeLz last updated on 19/Mar/23 $${V}\:=\:\left({r}_{\mathrm{1}} +\mathrm{2}\right)×\left({r}_{\mathrm{2}} +\mathrm{2}\right)×\left({r}_{\mathrm{3}} +\mathrm{2}\right)\:=\:{r}_{\mathrm{1}} {r}_{\mathrm{2}} {r}_{\mathrm{3}} +\mathrm{2}\left({r}_{\mathrm{1}} {r}_{\mathrm{2}} +{r}_{\mathrm{1}}…