Category: Arithmetic

Question Number 120847 by Jamshidbek2311 last updated on 03/Nov/20 $$Ifx,y,zthenprovethefollowing$$$$inequality$$$$(x^2+2)(y^2+2)(z^2+2)=9(xy+yz+xz)$$ Commented by Jamshidbek2311 last updated on…

Question Number 120800 by mathocean1 last updated on 02/Nov/20 $$whatremainwhenwedivise$$$${2222}^{3333}by{3333}^{2222}$$ Commented by prakash jain last updated on 03/Nov/20 https://www.wolframalpha.com/input/?i=2222%5E3333+%28mod+3333%5E2222%29 Terms…

Question Number 120654 by peter frank last updated on 01/Nov/20 $${\int }_0^{\mathrm{\infty }}\frac{\mathrm{dx}}{{[\mathrm{x}+\sqrt{1+{\mathrm{x}}^2}]}^{\mathrm{n}}}$$ Answered by mindispower last updated on 01/Nov/20 $${x}={sh}\left({t}\right),{n}>\mathrm{1}…

Question Number 120560 by peter frank last updated on 01/Nov/20 Answered by mathmax by abdo last updated on 01/Nov/20 $$\mathrm{I}=\int \frac{{\sin }^2\mathrm{x}}{1+{\cos }^2\mathrm{x}}\mathrm{dx}\Rightarrow \mathrm{I}=\int \frac{\frac{1-\cos \left(2\mathrm{x}\right)}{2}}{1+\frac{1+\cos \left(2\mathrm{x}\right)}{2}}\mathrm{dx}=\int \frac{2-\cos \left(2\mathrm{x}\right)}{3+\cos \left(2\mathrm{x}\right)}\mathrm{dx}$$$$=_{\mathrm{tanx}=\mathrm{t}} \:\:\:\:\int\:\:\frac{\mathrm{2}−\frac{\mathrm{1}−\mathrm{t}^{\mathrm{2}}…

Question Number 120363 by Lordose last updated on 30/Oct/20 $$$$$$\mathrm{Determine}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}1\mathrm{st}\mathrm{nth}\mathrm{term}$$$$\mathrm{of}\mathrm{the}\mathrm{Sequence}$$$$$$$$1,4,10,22,46,\dots .$$$$$$$$★\mathrm{Almighty}\mathrm{Formula}$$ Answered…