Category: Algebra

Question Number 217733 by Samuel12 last updated on 19/Mar/25 Answered by vnm last updated on 19/Mar/25 $$x^{\frac{1}{\ln (e^x-1)}}=e^{\frac{\ln x}{\ln (e^x-1)}}=e^{\frac{\ln x}{\ln x+\ln \frac{e^x-1}{x}}}=$$$${e}^{\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{ln}\:{x}}\mathrm{ln}\:\frac{{e}^{{x}}…

Question Number 217730 by ArshadS last updated on 19/Mar/25 $$x+\frac{1}{x}=3;x^5+\frac{1}{x^5}=?$$ Answered by Wuji last updated on 19/Mar/25 $${let}\:{S}_{{n}} ={x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }…

Question Number 217660 by ArshadS last updated on 17/Mar/25 $$f\left(x\right)+f\left(y\right)=f(x+y)+xy$$$$f\left(x\right)=?$$ Answered by vnm last updated on 19/Mar/25 $$f\left(x\right)+f\left(0\right)=f(x+0)+x\cdot 0\Rightarrow f\left(0\right)=0$$$${f}\left({x}\right)+{f}\left(−{x}\right)={f}\left({x}−{x}\right)+{x}\left(−{x}\right)=−{x}^{\mathrm{2}} \…

Question Number 217643 by Rojarani last updated on 17/Mar/25 $$a^{\frac{1}{3}}+b^{\frac{1}{3}}+c^{\frac{1}{3}}=\frac{1}{3^{\frac{1}{3}}-2^{\frac{1}{3}}}$$$$b+c-a=?$$ Answered by mehdee7396 last updated on…

Question Number 217579 by Rasheed.Sindhi last updated on 16/Mar/25 $$\mathrm{f}:\mathbb{R}\to \mathbb{R}$$$$\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)={\mathrm{x}}^2-\mathrm{x}+1$$$$\mathrm{f}\left(\mathrm{x}\right)=?$$$$\text{You can't use 'macro parameter character \#' in math mode}$$ Commented by Ghisom last updated on…