Question Number 211700 by hardmath last updated on 16/Sep/24 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{4}} −\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{3x}−\mathrm{6} \\ $$$$\mathrm{price}\:\mathrm{range}:\:\mathrm{E}\left(\mathrm{f}\right)\:=\:? \\ $$ Commented by Frix last updated on 16/Sep/24 $$\mathrm{What}\:\mathrm{do}\:“\mathrm{price}\:\mathrm{range}''\:\mathrm{and}\:“{E}\left({f}\right)''\:\mathrm{mean}?…
Question Number 211675 by MrGaster last updated on 16/Sep/24 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{x}}^{\mathrm{2}} =\mathrm{2}^{\boldsymbol{{x}}} \\ $$$$\:\mathrm{Find}\:\mathrm{more}\:\mathrm{than}\:\mathrm{three}\:\mathrm{solutions} \\ $$$$ \\ $$ Commented by mr W…
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…