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Category: Algebra

Question-100597

Question Number 100597 by bobhans last updated on 27/Jun/20 Commented by Dwaipayan Shikari last updated on 27/Jun/20 $${x}+\mathrm{2}\mid{y}\mid=\mathrm{3} \\ $$$${First}\:{case}\:\:\:\:{x}+\mathrm{2}{y}=\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}−\mathrm{3}{y}=\mathrm{5}\:\:\:\Rightarrow\mathrm{5}{y}=−\mathrm{2}\:\:\Rightarrow{y}=−\frac{\mathrm{2}}{\mathrm{5}}\:\:\:\:{x}=\frac{\mathrm{19}}{\mathrm{5}} \\ $$$${x}−{y}=\frac{\mathrm{21}}{\mathrm{5}}\:\:\:\:\:\:\begin{cases}{{x}=\frac{\mathrm{19}}{\mathrm{5}}}\\{{y}=−\frac{\mathrm{2}}{\mathrm{5}}}\end{cases} \\…

let-p-x-1-jx-n-1-jx-n-1-find-the-roots-of-p-x-2-factorize-p-x-inside-C-x-j-e-i-2pi-3-

Question Number 35056 by math khazana by abdo last updated on 14/May/18 $${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{jx}\right)^{{n}} \:−\left(\mathrm{1}−{jx}\right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$${j}\:={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \:. \\ $$ Commented by…

If-the-coefficients-of-x-k-and-x-k-1-in-the-expansion-2-3x-19-are-equal-what-is-the-value-of-k-

Question Number 100587 by bobhans last updated on 27/Jun/20 $$\mathrm{If}\:\mathrm{the}\:\mathrm{coefficients}\:\mathrm{of}\:{x}^{{k}} \:\mathrm{and}\:{x}^{{k}+\mathrm{1}} \:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{expansion}\:\left(\mathrm{2}+\mathrm{3}{x}\right)^{\mathrm{19}} \:\mathrm{are}\:\mathrm{equal}\:,\:\mathrm{what}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{k}\:? \\ $$ Commented by bobhans last updated on…

Question-166102

Question Number 166102 by Tawa11 last updated on 13/Feb/22 Answered by mr W last updated on 13/Feb/22 $${we}\:{have}\:{totally}\:\mathrm{12}\:{rolls}\:{for}\:{the}\:{numbers} \\ $$$$\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\:{the}\:{sum}\:{of}\:{them}\:{is}\:\mathrm{47}.\: \\ $$$${only}\:{one}\:{number}\:{occurs}\:\mathrm{3}\:{times}.\:{it}'{s} \\ $$$${easy}\:{to}\:{get}\:{that}\:{an}\:{other}\:{number}\:{must} \\…

x-yz-42-y-xz-6-z-xy-30-find-x-y-z-

Question Number 100567 by bramlex last updated on 27/Jun/20 $$\begin{cases}{{x}−\sqrt{{yz}}\:=\:\mathrm{42}}\\{{y}−\sqrt{{xz}}\:=\:\mathrm{6}}\\{{z}−\sqrt{{xy}}\:=\:−\mathrm{30}}\end{cases} \\ $$$${find}\:{x}+{y}+{z}\:= \\ $$ Commented by Dwaipayan Shikari last updated on 27/Jun/20 $$\mathrm{x}=\mathrm{54} \\ $$$$\mathrm{y}=\mathrm{24}\:\:\:\:\:\mathrm{z}=\mathrm{6}…