Category: Algebra

Question Number 216919 by Abdullahrussell last updated on 24/Feb/25 Answered by Wuji last updated on 24/Feb/25 $${\alpha }^3-3{\alpha }^2+5\alpha -17=0-----1$$$${\beta }^3-3{\beta }^2+5\beta +11=0-----2$$$$\left(\mathrm{1}\right)+\left(\mathrm{2}\right)…

Question Number 216900 by MathematicalUser2357 last updated on 24/Feb/25 Commented by MathematicalUser2357 last updated on 24/Feb/25 Is this right? (Part 2) - Complex number to the power of complex number Sorry for solving too complicated. But I was trying to solve clearly. Added more equivalent solution step from the last solution step and graph. The red one is the fixed one. Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 216841 by hardmath last updated on 22/Feb/25 $$\mathrm{Prove}\mathrm{that}:\delta \left(\mathrm{n}\right)=\sum _{\frac{\mathbf{d}}{\mathbf{n}}}\mathit{\phi }\left(\mathrm{d}\right)\mathit{\tau }\left(\frac{\mathrm{n}}{\mathrm{d}}\right)$$$$\mathit{\delta }\left(\mathrm{n}\right)=\sum _{\frac{\mathbf{d}}{\mathbf{n}}}\mathrm{d},\mathit{\tau }\left(\mathrm{n}\right)=\sum _{\frac{\mathbf{d}}{\mathbf{n}}}l\mathrm{and}\phi -\mathrm{Eyler}.\mathrm{f}$$ Answered by MrGaster last updated on 23/Feb/25 $$\mathrm{Let}\:{f}\left({n}\right)=\underset{{d}\mid{n}}…

Question Number 216785 by universe last updated on 20/Feb/25 $$\mathrm{given}\mathrm{the}\mathrm{recursive}\left\{{\mathrm{a}}_{\mathrm{n}}\right\}\mathrm{define}\mathrm{by}\mathrm{setting}$$$${\mathrm{a}}_1\in (0,1),{\mathrm{a}}_{\mathrm{n}+1}={\mathrm{a}}_{\mathrm{n}}(1-{\mathrm{a}}_{\mathrm{n}}),\mathrm{n}⩾1$$$$\mathrm{prove}\mathrm{that}\left(1\right)\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }{\mathrm{na}}_{\mathrm{n}}=1$$$$\:\:\left(\mathrm{2}\right)\:\:\mathrm{b}_{\mathrm{n}} \:=\:\mathrm{n}\left(\mathrm{1}−\mathrm{na}_{\mathrm{n}} \right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{incresing}\:\mathrm{sequence}…

Question Number 216734 by mnjuly1970 last updated on 17/Feb/25 Answered by sniper237 last updated on 18/Feb/25 $$LetE=\{f:A\to B\},\mid E\mid =3^m$$$$E\mathrm{\setminus }S=\{f\in E,\mid f\left(A\right)\mid =1or2\}$$$$\mid{E}\backslash{S}\mid=\:{C}_{\mathrm{3}} ^{\mathrm{1}} .\mathrm{1}^{{m}} +{C}_{\mathrm{3}}…