Category: Algebra

Question Number 140606 by mathsuji last updated on 10/May/21 $${(1+x)}^{2023}{(1-x+x^2)}^{2022}=a_0+a_{1}x+a_2{x}^2+\dots +a_{6067}{x}^{6067}$$$$alsoiftheequations$$$${a}_{{n}} \equiv\:\mathrm{1}\left({mod}\:\mathrm{5}\right)\:,\:{a}_{{n}} \equiv\:\mathrm{2}\left({mod}\:\mathrm{5}\right)\:,\:{n}=\mathrm{0};\mathrm{1};\mathrm{2};…;\mathrm{6067} \…

Question Number 140604 by ajfour last updated on 10/May/21 $$y=x^3-x-c;findtheroots.$$$$0⩽c⩽\frac{2}{3\sqrt{3}}$$ Answered by ajfour last updated on 11/May/21 Commented by ajfour…

Question Number 9532 by FilupSmith last updated on 14/Dec/16 $$S=\underset{n=t}{\sum ^k}(2n-1)$$$$S=?$$ Commented by sou1618 last updated on 14/Dec/16 $${S}=\left\{\underset{{n}=\mathrm{1}} {\overset{{k}}…

Question Number 140589 by bramlexs22 last updated on 09/May/21 $$x^{-\log {}_{2}x+4}<\frac{x}{16}$$ Answered by MJS_new last updated on 10/May/21 $${x}^{\mathrm{4}−\mathrm{log}_{\mathrm{2}} \:{x}} \in\mathbb{R}\:\Rightarrow\:{x}>\mathrm{0} \…

Question Number 9510 by FilupSmith last updated on 11/Dec/16 $$\mathrm{Prove}\mathrm{if}\mathrm{a}\mathrm{rational}\mathrm{times}\mathrm{an}\mathrm{irrational}$$$$\mathrm{can}\mathrm{result}\mathrm{in}\mathrm{a}\mathrm{rational}.$$ Answered by geovane10math last updated on 11/Dec/16 $$Arationaltimesanirrational\mathit{a}\mathit{l}\mathit{y}\mathit{a}\mathit{w}\mathit{s}$$$${is}\:{a}\:{irrational}.\: \…