Category: Algebra

Question Number 15570 by tawa tawa last updated on 11/Jun/17 $$\mathrm{Solve}:2^{\mathrm{x}}={\mathrm{x}}^4$$ Commented by tawa tawa last updated on 11/Jun/17 $$\mathrm{workings}$$…

Question Number 146635 by mathdanisur last updated on 14/Jul/21 $$\underset{x\to \mathrm{\infty }}{lim}{\left(\frac{2x+1}{x+1}\right)}^{\frac{1}{\mathit{x}}}=?$$ Answered by Olaf_Thorendsen last updated on 14/Jul/21 $$\frac{1}{x}\ln \left(\frac{2x+1}{x+1}\right)=\frac{1}{x}[\ln (2+x)-\ln (x+1)]$$$$=\:\frac{\mathrm{1}}{{x}}\left[\mathrm{ln2}+\mathrm{ln}{x}+\mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}{x}}\right)−\mathrm{ln}{x}−\mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\right] \…

Question Number 146622 by mathdanisur last updated on 14/Jul/21 $$\frac{1}{\sqrt[8]{6}+1}\cdot \frac{1}{\sqrt[4]{6}+1}\cdot \frac{1}{\sqrt{6}+1}+1=?$$ Commented by hknkrc46 last updated on 14/Jul/21 $$★\frac{1}{(\sqrt[8]{6}+1)(\sqrt[4]{6}+1)(\sqrt{6}+1)}+1$$$$=\frac{\sqrt[8]{6}-1}{\underset{\sqrt[4]{6}-1}{\underbrace{(\sqrt[8]{6}-1)(\sqrt[8]{6}+1)}}(\sqrt[4]{6}+1)(\sqrt{6}+1)}+1$$$$=\:\frac{\sqrt[{\mathrm{8}}]{\mathrm{6}}\:−\:\mathrm{1}}{\underset{\sqrt{\mathrm{6}}\:−\:\mathrm{1}}…

Question Number 146611 by mathdanisur last updated on 14/Jul/21 $$y=x^2+x,y=2x^2+x+mandy=kx+b$$$$ifonepointintersects,findk\cdot b=?$$ Answered by mr W last updated on 14/Jul/21 $${y}={x}^{\mathrm{2}}…

Question Number 146606 by iloveisrael last updated on 14/Jul/21 Answered by som(math1967) last updated on 14/Jul/21 $$x+\sqrt{x^2-1}+\frac{1}{x-\sqrt{x^2-1}}=20$$$$\frac{{x}^{\mathrm{2}} −{x}^{\mathrm{2}} +\mathrm{1}+\mathrm{1}}{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}=\mathrm{20} \…