Category: Algebra

Question Number 155272 by bekzodjumayev last updated on 28/Sep/21 Commented by bekzodjumayev last updated on 28/Sep/21 $$\mathit{P}rovethat$$$$Pleasehelp$$ Commented by puissant last…

Question Number 155244 by mathdanisur last updated on 27/Sep/21 $$\mathrm{Solve}\mathrm{the}\mathrm{equation}:$$$$$$$${\left(\sin \mathbf{x}\right)}^3+\sin \mathbf{x}=\cos \mathbf{x}$$ Answered by ajfour last updated on 27/Sep/21 $$\mathrm{tan}\:{x}\left(\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{tan}\:^{\mathrm{2}}…

Question Number 155231 by mnjuly1970 last updated on 27/Sep/21 $$$$$$f\left(x\right):=\sqrt{\frac{1}{a}+x}-\sqrt{\frac{1}{a}-x}$$$$and{\mathrm{D}}_f\ne \varnothing ,$$$$g\left(x\right)=\sqrt{\frac{ax-1}{f^{-1}(ax-a)}}$$$$find:{\mathrm{D}}_g=?$$ Terms of…

Question Number 24142 by Tinkutara last updated on 13/Nov/17 $$Provethat$$$$\underset{r=1}{\sum ^{2n-1}}{(-1)}^{r-1}\left(\underset{0}{\stackrel{1}{\int }}{x}^r{(1-x)}^{2n-r}dx\right)$$$$=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left[\left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}} +{x}^{\mathrm{2}{n}} −\left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}+\mathrm{1}}…

Question Number 155204 by mathdanisur last updated on 26/Sep/21 $$\mathrm{Solve}\mathrm{for}\mathrm{positive}\mathrm{integers}:$$$$\mathrm{abcd}+\mathrm{abc}=(\mathrm{a}+1)(\mathrm{b}+1)(\mathrm{c}+1)$$ Answered by MJS_new last updated on 27/Sep/21 $$a⩽b⩽c$$$$\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions}\:\mathrm{for}\:{a}\:{b}\:{c}\:{d}\:\mathrm{are} \…