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Category: Algebra

Resoudre-le-systeme-d-equations-x-y-xy-84-x-2-y-2-25-

Question Number 213721 by a.lgnaoui last updated on 14/Nov/24 $$\boldsymbol{\mathrm{Resoudre}}\:\boldsymbol{\mathrm{le}}\:\boldsymbol{\mathrm{systeme}}\:\boldsymbol{\mathrm{d}}'\:\boldsymbol{\mathrm{equations}}: \\ $$$$\begin{cases}{\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\right)\boldsymbol{\mathrm{xy}}=\mathrm{84}}\\{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} \:\:\:\:\:\:=\mathrm{25}}\end{cases} \\ $$ Answered by golsendro last updated on 14/Nov/24 $$\:\:\:\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2}} −\mathrm{2xy}=\:\mathrm{x}^{\mathrm{2}}…

Find-sin-2-7-44-22-54-800-

Question Number 213693 by hardmath last updated on 13/Nov/24 $$\mathrm{Find}: \\ $$$$\mathrm{sin}^{\mathrm{2}} \:\left(\mathrm{7}°\:\mathrm{44}'\:\mathrm{22},\mathrm{54}''\right)\centerdot\mathrm{800} \\ $$ Commented by Ghisom last updated on 13/Nov/24 $$\mathrm{use}\:\mathrm{a}\:\mathrm{calculator} \\ $$$$\approx\mathrm{14}.\mathrm{5090174}…

Question-213688

Question Number 213688 by Abdullahrussell last updated on 13/Nov/24 Answered by mr W last updated on 13/Nov/24 $${at}\:{x}_{{min}} =−\mathrm{2}: \\ $$$$−\mathrm{2}+{y}=\mathrm{4}\sqrt{{y}+\mathrm{3}} \\ $$$${y}+\mathrm{3}−\mathrm{4}\sqrt{{y}+\mathrm{3}}−\mathrm{5}=\mathrm{0} \\ $$$$\left(\sqrt{{y}+\mathrm{3}}+\mathrm{1}\right)\left(\sqrt{{y}+\mathrm{3}}−\mathrm{5}\right)=\mathrm{0}…

Question-213641

Question Number 213641 by Abdullahrussell last updated on 12/Nov/24 Answered by Ghisom last updated on 03/Dec/24 $$\alpha_{{k}} \in\mathbb{Z} \\ $$$${p}\left({x}\right)=\underset{{k}=\mathrm{3}} {\overset{{n}} {\sum}}\alpha_{{k}} {x}^{{k}} \\ $$$${x}\in\mathbb{Z}\:\Rightarrow\:{p}\left({x}\right)\in\mathbb{Z}…

Question-213639

Question Number 213639 by efronzo1 last updated on 12/Nov/24 Answered by golsendro last updated on 12/Nov/24 $$\:\:\:\mathrm{8}^{\mathrm{x}} =\mathrm{25}^{\mathrm{y}} =\:\mathrm{t}\:\Rightarrow\begin{cases}{\mathrm{x}=\:\mathrm{log}\:_{\mathrm{8}} \mathrm{t}}\\{\mathrm{y}=\:\mathrm{log}\:_{\mathrm{25}} \mathrm{t}}\end{cases} \\ $$$$\:\:\Rightarrow\mathrm{8}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{25}\left(\frac{\mathrm{1}}{\mathrm{y}}\right)=\:\mathrm{1} \\ $$$$\:\:\:\mathrm{8}.\:\mathrm{log}\:_{\mathrm{t}}…

x-3-5x-42-x-3-P-x-Find-P-3-

Question Number 213624 by hardmath last updated on 10/Nov/24 $$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{5x}\:−\:\mathrm{42}\:=\:\left(\mathrm{x}\:−\:\mathrm{3}\right)\centerdot\mathrm{P}\left(\mathrm{x}\right) \\ $$$$\mathrm{Find}:\:\:\:\mathrm{P}\left(\mathrm{3}\right)\:=\:? \\ $$ Answered by A5T last updated on 10/Nov/24 $$\left({x}−\mathrm{3}\right)\left({x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{14}\right)−\left({x}−\mathrm{3}\right){P}\left({x}\right)=\mathrm{0} \\…