Question Number 211680 by RojaTaniya last updated on 16/Sep/24 $$\:{x},\:{y}\:{are}\:{positive}\:{integer}\:{such}\: \\ $$$$\:\:{that},\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{xy}=\mathrm{911}.\:\left({x},{y}\right)=? \\ $$ Commented by AlagaIbile last updated on 16/Sep/24 $$\:{That}'{s}\:{a}\:{symmetric}\:{Function} \\…
Question Number 211634 by BaliramKumar last updated on 15/Sep/24 Answered by golsendro last updated on 15/Sep/24 $$\:\mathrm{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:=\:\frac{\mathrm{64}+\mathrm{1}}{\mathrm{8}}\:=\:\mathrm{2}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} } \\ $$$$\:\mathrm{y}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{3}} }\:=\:\frac{\mathrm{729}+\mathrm{1}}{\mathrm{27}}=\:\mathrm{3}^{\mathrm{3}}…
Question Number 211657 by hardmath last updated on 15/Sep/24 $$\mathrm{sin}\left(\mathrm{9x}\right)\:=\:\mathrm{sin}\left(\mathrm{5x}\right)\:+\:\mathrm{sin}\left(\mathrm{3x}\right) \\ $$$$\mathrm{find}:\:\:\mathrm{x}\:=\:? \\ $$ Answered by Frix last updated on 15/Sep/24 $$\mathrm{sin}\:\left(\left(\mathrm{2}{n}+\mathrm{1}\right){x}\right)\:=\mathrm{sin}\:{x}\:\left(\mathrm{1}+\mathrm{2}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\mathrm{cos}\:\left(\mathrm{2}{kx}\right)\right) \\…
Question Number 211659 by efronzo1 last updated on 15/Sep/24 Commented by Frix last updated on 15/Sep/24 $$\mathrm{Simply}\:\mathrm{transform}\:\mathrm{it}\:\Rightarrow\:{n}=\mathrm{3} \\ $$ Answered by BHOOPENDRA last updated on…
Question Number 211658 by efronzo1 last updated on 15/Sep/24 $$\:\:\:\underbrace{\:} \\ $$ Answered by mehdee1342 last updated on 15/Sep/24 $${y}=\sqrt{\mathrm{19}−\mathrm{8}\sqrt{\mathrm{3}}}\Rightarrow{y}^{\mathrm{2}} =\mathrm{19}−\mathrm{8}\sqrt{\mathrm{3}} \\ $$$${y}^{\mathrm{4}} −\mathrm{18}{y}^{\mathrm{2}} +\mathrm{361}=\mathrm{192}…
Question Number 211598 by MrGaster last updated on 14/Sep/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{{x}}+\mathrm{3}<\mathrm{0}}\\{\frac{\mathrm{2}\boldsymbol{{x}}−\mathrm{1}}{\boldsymbol{{x}}+\mathrm{2}}\geq\mathrm{1}}\end{cases} \\ $$$$ \\ $$ Answered by A5T last updated on 14/Sep/24 $${x}^{\mathrm{2}}…
Question Number 211614 by hardmath last updated on 14/Sep/24 $$ \\ $$A group of people are standing in a circle. Every second person is removed…
Question Number 211597 by MrGaster last updated on 14/Sep/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\boldsymbol{{x}}^{\mathrm{4}} −\mathrm{4}\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{22}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{24}\boldsymbol{{x}}+\mathrm{36}=\mathrm{0} \\ $$$$ \\ $$ Answered by Ghisom last updated on…
Question Number 211605 by MrGaster last updated on 14/Sep/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Let}\:\boldsymbol{{a}}_{\mathrm{1}} ,\boldsymbol{{a}}_{\mathrm{2}} ,\ldots\boldsymbol{{a}}_{\boldsymbol{{n}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Is}\:\mathrm{n}\:\mathrm{real}\:\mathrm{numbers}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{All}\:\mathrm{fall}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval}\:\left(−\mathrm{1},\mathrm{1}\right) \\ $$$$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ $$$$\left(\mathrm{1}\right)\mathrm{Prove}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{1}\leq\boldsymbol{{i}},\boldsymbol{{j}}\leq\boldsymbol{{n}}} {\prod}\frac{\mathrm{1}+\boldsymbol{{a}}_{\boldsymbol{{i}}} \boldsymbol{{a}}_{\boldsymbol{{j}}} }{\mathrm{1}−\boldsymbol{{a}}_{\boldsymbol{{i}}}…
Question Number 211601 by MrGaster last updated on 14/Sep/24 $$ \\ $$$$\:\:\:\:\:\:\:\mathrm{set}\:\boldsymbol{\alpha}\sqrt[{\mathrm{3}}]{\mathrm{2}},\mathrm{ask}\:\mathbb{Q}\left(\boldsymbol{\alpha}\right)\mathrm{Upper}\:\mathrm{irreducible}\:\mathrm{cubic}\:\mathrm{equation}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{3}\boldsymbol{{x}}+\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{All}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of} \\ $$$$ \\ $$ Terms of Service Privacy…