Category: Algebra

Question Number 163902 by HongKing last updated on 11/Jan/22 $$\sqrt{\mathrm{x}{!}^{\mathbf{x}!}}+2^{\mathbf{x}!}=\mathrm{x}{!}^3+10\mathrm{x}!+4$$$$\mathrm{find}:\mathbf{x}=?$$ Answered by MJS_new last updated on 11/Jan/22 $${x}!\:\mathrm{is}\:\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{N}\:\Rightarrow\:\mathrm{try}\:\mathrm{the}\:\mathrm{first}\:\mathrm{few}……

Question Number 163891 by HongKing last updated on 11/Jan/22 $$\mathrm{if}\mathrm{f}({\mathrm{x}}^3+1)={\mathrm{x}}^5+4\mathrm{x}+2$$$$\mathrm{find}\underset{0}{\stackrel{1}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=?$$ Answered by Ar Brandon last updated on…

Question Number 163861 by mathlove last updated on 11/Jan/22 Answered by Ar Brandon last updated on 11/Jan/22 $$x=\sqrt{5}+\frac{1}{x}\Rightarrow x=\frac{\sqrt{5}\pm \sqrt{9}}{2}=\frac{\sqrt{5}+3}{2}(x>0,\sqrt{5}-3<0)$$ Terms of Service Privacy Policy…

Question Number 32788 by rahul 19 last updated on 02/Apr/18 $$\mathit{T}heleastpositiveintegralvalueof$$$${}^{\prime }{x}^{\prime }satisfying:$$$$(e^x-2)\left(\sin (x+\frac{\pi }{4})\right)(x-{\log }_e\underset{}{2})(sinx-cosx)<0$$ Commented by rahul 19 last…

Question Number 163849 by alephzero last updated on 11/Jan/22 $$\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\dots \frac{1}{19\cdot 20}+\frac{1}{20\cdot 21}=?$$ Answered by cortano1 last updated on 11/Jan/22 $$\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{20}} {\sum}}\:\frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)}\:=\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{20}} {\sum}}\:\left(\frac{\mathrm{1}}{{k}}−\frac{\mathrm{1}}{{k}+\mathrm{1}}\right) \…