Question Number 162181 by bobhans last updated on 27/Dec/21 $$\:\:\:\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}\: \\ $$$$\:\:\:\:\:\left.\begin{matrix}{\mathrm{x}^{\mathrm{4}} −\mathrm{2x}+\mathrm{y}=\mathrm{y}^{\mathrm{4}} }\\{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \right)^{\mathrm{3}} \:=\:\mathrm{3}}\end{matrix}\right\}\: \\ $$ Commented by benhamimed last updated on…
Question Number 162165 by cortano last updated on 27/Dec/21 $$\mathrm{If}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{equation} \\ $$$$\:{ax}^{\mathrm{2}} +\mathrm{2}{bx}+{c}=\mathrm{0}\:\mathrm{is}\:\mathrm{same}\:\mathrm{as}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\:\mathrm{of}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{px}^{\mathrm{2}} +\mathrm{2}{qx}+{r}=\mathrm{0}\:\mathrm{where} \\ $$$$\:{a},{b},{c},{p}\:,{r}\:\mathrm{are}\:\mathrm{non}\:\mathrm{zero}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\frac{{b}^{\mathrm{2}} }{{q}^{\mathrm{2}} }\right)\left(\frac{{p}}{{a}}\right)\left(\frac{{r}}{{c}}\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\: \\…
Question Number 96584 by Jidda28 last updated on 04/Jun/20 Commented by mr W last updated on 03/Jun/20 $${when}\:{posting}\:{an}\:{image}\:{you}\:{should} \\ $$$${crop}\:{the}\:{image}\:{properly}\:{or}\:{diasable} \\ $$$${crop}. \\ $$ Commented…
Question Number 31047 by abdo imad last updated on 02/Mar/18 $${let}\:\Delta=\left\{\left({x},{y}\right)\in{N}^{\mathrm{2}} \:/{x}+{y}={n}\:,\:{n}\in{N}\right\}\:{find}\:{card}\Delta \\ $$$$\left.\mathrm{2}\right)\:{let}\:{A}=\:\left\{\left({x},{y}\right)\in{N}^{\mathrm{2}} /\:{x}+\mathrm{2}{y}={n}\right\}\:{find}\:{card}\:{A}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31046 by abdo imad last updated on 02/Mar/18 $${prove}\:{that}\:{C}_{{n}} ^{{o}} \:{C}_{{n}} ^{{p}} \:+{C}_{{n}} ^{\mathrm{1}} \:{C}_{{n}−\mathrm{1}} ^{{p}−\mathrm{1}} \:+…{C}_{{n}} ^{{p}} \:{C}_{{n}−{p}} ^{\mathrm{0}} =\mathrm{2}^{{p}} \:{C}_{{n}} ^{{p}}…
Question Number 31042 by abdo imad last updated on 02/Mar/18 $${solve}\:{in}\:{N}^{\mathrm{2}} \:\:\mathrm{9}{y}^{\mathrm{2}} \:−\left({x}+\mathrm{1}\right)^{\mathrm{2}} =\mathrm{32}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31040 by abdo imad last updated on 02/Mar/18 $${solve}\:{in}\:{Z}^{\mathrm{2}} \:{x}^{\mathrm{2}} \:−{y}^{\mathrm{2}} =\mathrm{1969} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31041 by abdo imad last updated on 02/Mar/18 $${solve}\:{in}\:{Z}^{\mathrm{2}} \:\mathrm{11}{x}\:−\mathrm{5}{y}\:=\mathrm{14} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31039 by abdo imad last updated on 02/Mar/18 $${find}\:{the}\:{sum} \\ $$$${s}_{\mathrm{0}} =\:{C}_{{n}} ^{{o}} \:+{C}_{{n}} ^{\mathrm{4}} \:+{C}_{{n}} ^{\mathrm{8}} \:+… \\ $$$${s}_{\mathrm{1}} =\:{C}_{{n}} ^{\mathrm{1}} \:+{C}_{{n}}…
Question Number 31037 by abdo imad last updated on 02/Mar/18 $${let}\:\:\theta\in\left[\mathrm{0},\pi\right]\:\:{and}\:{Z}=\mathrm{1}+{cos}\theta\:+{isin}\theta \\ $$$${Z}^{'} ={cos}\theta\:+\left(\mathrm{1}+{sin}\theta\right){i}\:\:{find}\:\mid{ZZ}^{'} \mid\:\:{arg}\left({ZZ}^{'} \right) \\ $$$$\mid\frac{{Z}}{{Z}^{'} }\mid\:,\:{arg}\left(\frac{{Z}}{{Z}^{,} }\right)\:\:,\:\:\mid{Z}−{Z}^{,} \mid\:{and}\:{arg}\left({Z}−{Z}^{,} \right). \\ $$ Terms…