Category: Algebra

Question Number 211680 by RojaTaniya last updated on 16/Sep/24 $$x,yarepositiveintegersuch$$$$that,x^3+y^3+xy=911.(x,y)=?$$ Commented by AlagaIbile last updated on 16/Sep/24 $$\:{That}'{s}\:{a}\:{symmetric}\:{Function} \…

Question Number 211657 by hardmath last updated on 15/Sep/24 $$\sin \left(9\mathrm{x}\right)=\sin \left(5\mathrm{x}\right)+\sin \left(3\mathrm{x}\right)$$$$\mathrm{find}:\mathrm{x}=?$$ Answered by Frix last updated on 15/Sep/24 $$\mathrm{sin}\:\left(\left(\mathrm{2}{n}+\mathrm{1}\right){x}\right)\:=\mathrm{sin}\:{x}\:\left(\mathrm{1}+\mathrm{2}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\mathrm{cos}\:\left(\mathrm{2}{kx}\right)\right) \…

Question Number 211658 by efronzo1 last updated on 15/Sep/24 $$\underbrace{}$$ Answered by mehdee1342 last updated on 15/Sep/24 $$y=\sqrt{19-8\sqrt{3}}\Rightarrow y^2=19-8\sqrt{3}$$$${y}^{\mathrm{4}} −\mathrm{18}{y}^{\mathrm{2}} +\mathrm{361}=\mathrm{192}…

Question Number 211614 by hardmath last updated on 14/Sep/24 $$$$A group of people are standing in a circle. Every second person is removed…

Question Number 211605 by MrGaster last updated on 14/Sep/24 $$\mathrm{Let}{\mathit{a}}_1,{\mathit{a}}_2,\dots {\mathit{a}}_{\mathit{n}}$$$$\mathrm{Is}\mathrm{n}\mathrm{real}\mathrm{numbers}.$$$$\mathrm{All}\mathrm{fall}\mathrm{in}\mathrm{the}\mathrm{interval}(-1,1)$$$$\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$$$$\left(1\right)\mathrm{Prove}\mathrm{that}:$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{1}\leq\boldsymbol{{i}},\boldsymbol{{j}}\leq\boldsymbol{{n}}} {\prod}\frac{\mathrm{1}+\boldsymbol{{a}}_{\boldsymbol{{i}}} \boldsymbol{{a}}_{\boldsymbol{{j}}} }{\mathrm{1}−\boldsymbol{{a}}_{\boldsymbol{{i}}}…