Category: Algebra

Question Number 217541 by hardmath last updated on 15/Mar/25 $$\mathrm{f}:\mathbb{R}\to \mathbb{R}$$$$\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)={\mathrm{x}}^2-\mathrm{x}+1$$$$\mathrm{f}\left(0\right)=?$$ Answered by mr W last updated on 16/Mar/25…

Question Number 217482 by Rasheed.Sindhi last updated on 14/Mar/25 $${(n\sqrt{(n+1)}+(n+1)\sqrt{n})}^n+{(n\sqrt{(n+1)}-(n+1)\sqrt{n})}^n=n^2(n+1)(n+3)$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 217416 by peter frank last updated on 13/Mar/25 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 217389 by Simurdiera last updated on 12/Mar/25 $$\mathrm{Resolver}$$$$\frac{\mid x-1\mid +\mid x+2\mid }{\mid x\mid -1}\le 3$$ Answered by A5T last updated on 13/Mar/25 $$\mathrm{when}-2⩽\mathrm{x}<-1;\mid \mathrm{x}-1\mid =1-\mathrm{x},\mid \mathrm{x}+2\mid =\mathrm{x}+2\wedge \mid \mathrm{x}\mid =-\mathrm{x}$$$$\Rightarrow\frac{\mid\mathrm{x}−\mathrm{1}\mid+\mid\mathrm{x}+\mathrm{2}\mid}{\mid\mathrm{x}\mid−\mathrm{1}}\leqslant\mathrm{3}\Rightarrow\frac{\mathrm{1}−\mathrm{x}+\mathrm{x}+\mathrm{2}}{−\mathrm{x}−\mathrm{1}}\leqslant\mathrm{3} \…

Question Number 217381 by Rasheed.Sindhi last updated on 12/Mar/25 $$\mathrm{Let}\mathrm{a},\mathrm{b},\mathrm{c}\mathrm{be}\mathrm{real}\mathrm{numbers}\mathrm{satisfying}$$$$\mathrm{the}\mathrm{equations}$$$$\left(1\right)\mathrm{a}+\mathrm{b}+\mathrm{c}=4$$$$\left(2\right){\mathrm{a}}^3+{\mathrm{b}}^3+{\mathrm{c}}^3=34$$$$\mathrm{Find}\mathrm{ab}+\mathrm{bc}+\mathrm{ca}$$ Commented by…