Category: Algebra

Question Number 148229 by iloveisrael last updated on 26/Jul/21 Commented by nimnim last updated on 26/Jul/21 $$x+\sqrt{x^2-1}+\frac{1}{x-\sqrt{x^2-1}}=20$$$$\Rightarrow\frac{{x}^{\mathrm{2}} −\left({x}^{\mathrm{2}} −\mathrm{1}\right)+\mathrm{1}}{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}×\frac{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}+\sqrt{{x}^{\mathrm{2}}…

Question Number 148203 by liberty last updated on 26/Jul/21 $$\underset{n=1}{\sum ^{\mathrm{\infty }}}\left(\frac{8}{n^2+n}\right)=?$$ Answered by mathmax by abdo last updated on 26/Jul/21 $$\mathrm{S}=\mathrm{8}\sum_{\mathrm{n}=\mathrm{1}}…

Question Number 82665 by jagoll last updated on 23/Feb/20 $$\sqrt{6561\sqrt{6561\sqrt{6561\sqrt{6561\sqrt{\dots }}}}}=3^{8^x}$$$$\sqrt{6561\sqrt{\dots }}\left(60time\right)$$$$findx$$ Commented by mr W last updated on 23/Feb/20…

Question Number 148154 by mathdanisur last updated on 25/Jul/21 $$\sqrt{1!+2!+3!+\dots +\mathit{n}!}\in \mathbb{N}$$$$\mathit{n}=?$$ Answered by puissant last updated on 25/Jul/21 $$\mathrm{n}=1$$ Commented…

Question Number 82596 by peter frank last updated on 22/Feb/20 Commented by mr W last updated on 23/Feb/20 $$\left(a\right)$$$$ithinkthebeamwillstayinwater.$$$$\left(b\right)$$$${the}\:{beam}\:{will}\:{be}\:{partially}\:{reflected}…