Category: Algebra

Question Number 162068 by HongKing last updated on 25/Dec/21 Answered by Lordose last updated on 26/Dec/21 $$$$$$\Omega\:=\:\underset{\epsilon\rightarrow\mathrm{0}} {\mathrm{lim}}\int_{\mathrm{sin}^{−\mathrm{1}} \left(\epsilon\right)} ^{\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{1}−\epsilon\right)} \mathrm{log}\left(\left(\mathrm{cos}\left(\mathrm{x}\right)\right)^{\mathrm{cot}\left(\mathrm{x}\right)} \centerdot\left(\mathrm{sin}\left(\mathrm{x}\right)\right)^{\frac{\mathrm{cos}\left(\mathrm{x}\right)}{\mathrm{1}+\mathrm{sin}\left(\mathrm{x}\right)}}…

Question Number 96527 by student work last updated on 02/Jun/20 $$\mathrm{proof}\mathrm{that}{1}^2+2^2+3^2+\dots .+{\mathrm{n}}^2=\frac{\mathrm{n}(2\mathrm{n}+1)(\mathrm{n}+1)}{6}$$ Commented by 06122004 last updated on 02/Jun/20 Answered…

Question Number 162042 by HongKing last updated on 25/Dec/21 $$\mathrm{let}\mathrm{a};\mathrm{b};\mathrm{c}\in \mathbb{R}\mathrm{such}\mathrm{that}\mathrm{a}+\mathrm{b}+\mathrm{c}=3$$$$\mathrm{prove}\mathrm{that}:$$$${\mathrm{a}}^3+{\mathrm{b}}^3+{\mathrm{c}}^3⩾{\mathrm{a}}^3\mathrm{b}+{\mathrm{b}}^3\mathrm{c}+{\mathrm{c}}^3\mathrm{a}$$ Terms of Service…

Question Number 96505 by bemath last updated on 02/Jun/20 $$\frac{\sqrt{\sqrt[4]{8}-\sqrt{\sqrt{2}+1}}}{\sqrt{\sqrt[4]{8}+\sqrt{\sqrt{2}-1}}-\sqrt{\sqrt[4]{8}-\sqrt{\sqrt{2}-1}}}?$$ Commented by bemath last updated on 02/Jun/20 $$\mathrm{yes}\mathrm{sir}.\mathrm{you}\mathrm{are}\mathrm{right}$$ Commented by bobhans…

Question Number 30956 by Tinkutara last updated on 01/Mar/18 Answered by MJS last updated on 01/Mar/18 $$\left(3\right)\mathrm{because}n!\mid \underset{k=i}{\prod ^{i+n-1}}k;i\in \mathbb{N}$$ Commented by Tinkutara last…