Question Number 161951 by mathlove last updated on 24/Dec/21 $${x}^{{x}} =\mathrm{2}^{\mathrm{2048}} \\ $$$${x}=? \\ $$ Answered by aleks041103 last updated on 24/Dec/21 $$\mathrm{2048}=\mathrm{2}^{\mathrm{11}} \\ $$$$\Rightarrow{x}^{{x}}…
Question Number 161946 by mathlove last updated on 24/Dec/21 Answered by Rasheed.Sindhi last updated on 29/Dec/21 $${x}+{y}\left({x}+\mathrm{1}\right)=\mathrm{3}\Rightarrow{y}=\frac{\mathrm{3}−{x}}{{x}+\mathrm{1}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow{y}+\mathrm{1}=\frac{\mathrm{3}−{x}+{x}+\mathrm{1}}{{x}+\mathrm{1}}=\frac{\mathrm{4}}{{x}+\mathrm{1}} \\ $$$${y}+{z}\left({y}+\mathrm{1}\right)=\mathrm{5}\Rightarrow\frac{\mathrm{3}−{x}}{{x}+\mathrm{1}}+{z}\left(\frac{\mathrm{4}}{{x}+\mathrm{1}}\right)=\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\mathrm{3}−{x}+\mathrm{4}{z}=\mathrm{5}{x}+\mathrm{5}\Rightarrow{x}=\frac{\mathrm{2}{z}−\mathrm{1}}{\mathrm{3}} \\ $$$${z}+{x}\left({z}+\mathrm{1}\right)=\mathrm{7}\Rightarrow{z}+\left(\frac{\mathrm{2}{z}−\mathrm{1}}{\mathrm{3}}\right)\left({z}+\mathrm{1}\right)=\mathrm{7}…
Question Number 96407 by Enyz last updated on 01/Jun/20 Commented by prakash jain last updated on 01/Jun/20 $${z}^{\mathrm{3}} +\mathrm{2}{z}^{\mathrm{2}} +\left({k}−\mathrm{8}\sqrt{\mathrm{2}}{i}\right){z}+\left(\mathrm{8}−\mathrm{4}{k}\sqrt{\mathrm{2}}{i}\right)=\mathrm{0} \\ $$$$\mathrm{Let}\:{z}={x}\:\mathrm{be}\:\mathrm{real}\:\mathrm{root} \\ $$$${x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}}…
Question Number 30860 by ajfour last updated on 27/Feb/18 $${S}=\:\mathrm{3}\left(\mathrm{1}!\right)−\mathrm{4}\left(\mathrm{2}!\right)+\mathrm{5}\left(\mathrm{3}!\right)−\mathrm{6}\left(\mathrm{4}!\right)+…. \\ $$$$\:\:\:\:…..−\left(\mathrm{2008}\right)\left(\mathrm{2006}!\right)+\mathrm{2007}! \\ $$$${Find}\:{value}\:{of}\:{S}. \\ $$ Answered by MJS last updated on 27/Feb/18 $$\mathrm{3}\centerdot\mathrm{1}!−\mathrm{4}\centerdot\mathrm{2}!=−\mathrm{5}\:\left[=−\left(\mathrm{3}!−\mathrm{1}\right)\right] \\…
Question Number 161931 by mnjuly1970 last updated on 24/Dec/21 $$ \\ $$$$\:\:\:\:\:\:\mathrm{I}{f}\:\:\:\:\frac{\:\mathrm{1}−{sin}\left({x}\right)−{cos}\left({x}\right)}{\mathrm{1}+{sin}\left({x}\right)−{cos}\left({x}\right)}\:=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:{then}\:\:{find}\:{the}\:{value}\:{of}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{tan}\left({x}\right)\:+\:\frac{\mathrm{1}}{{cos}\left({x}\right)}\:=? \\ $$$$\:\:\:\:\:\: \\ $$$$ \\ $$ Commented by cortano…
Question Number 161930 by Rasheed.Sindhi last updated on 24/Dec/21 $$\begin{cases}{{a}_{\mathrm{0}} =−\mathrm{2}\:}\\{{a}_{{n}} ={a}_{{n}−\mathrm{1}} +\mathrm{2}{n}}\end{cases}\:\:\:\:\:;\:{a}_{{n}} =? \\ $$ Answered by mr W last updated on 24/Dec/21 $${a}_{{n}}…
Question Number 96390 by bemath last updated on 01/Jun/20 Answered by john santu last updated on 01/Jun/20 $$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{weight}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{initial}\:\mathrm{corn}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{weight} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{final}\:\mathrm{mixture}.\:\mathrm{therefore} \\ $$$$\left(\mathrm{20}\:\mathrm{bushels}\right)\frac{\mathrm{56}\:\mathrm{pounds}}{\mathrm{bushels}}\:+\:\left({x}\:\mathrm{bushels}\right)\frac{\mathrm{50}\:\mathrm{pounds}}{\mathrm{bushels}}\: \\…
Question Number 30849 by Penguin last updated on 27/Feb/18 $${x}^{\mathrm{7}} +{x}^{\mathrm{6}} +{x}^{\mathrm{5}} +{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}+\mathrm{1}=\mathrm{0} \\ $$$$\: \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{7}} {\sum}}\left[\Re\left({x}_{{k}} \right)\right]^{\mathrm{2}} \:=\:? \\…
Question Number 161914 by mnjuly1970 last updated on 24/Dec/21 $$\:\mathrm{If}\:, \\ $$$$\:\:\:{x}^{\:\mathrm{2}} \:+\:\mathrm{9}{y}^{\:\mathrm{2}} \:+\:\mathrm{4}{x}\:+\mathrm{18}{y}\:−\mathrm{23}=\mathrm{0} \\ $$$$ \\ $$$$\:{then}\:\:{find}\:{the}\:{value}\:\:{of}\:\:,\:\:\mathrm{M}_{\:} {ax}\:\left(\:\mathrm{3}{x}+\mathrm{2}{y}\:\right)\:. \\ $$$$\:−−−−−−−−− \\ $$$$ \\ $$…
Question Number 161900 by HongKing last updated on 23/Dec/21 $$\mathrm{0}<\mathrm{x};\mathrm{y};\mathrm{z}<\mathrm{1} \\ $$$$\left(\mathrm{1}-\mathrm{x}\right)\left(\mathrm{1}-\mathrm{y}\right)\left(\mathrm{1}-\mathrm{z}\right)=\mathrm{xyz} \\ $$$$\mathrm{Find}: \\ $$$$\Omega\:=\:\mathrm{min}\:\left(\frac{\mathrm{1}-\mathrm{x}}{\mathrm{xy}}\:+\:\frac{\mathrm{1}-\mathrm{y}}{\mathrm{yz}}\:+\:\frac{\mathrm{1}-\mathrm{z}}{\mathrm{zx}}\right) \\ $$ Answered by aleks041103 last updated on 24/Dec/21…