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Category: Algebra

Question-65087

Question Number 65087 by Tawa1 last updated on 25/Jul/19 Answered by MJS last updated on 25/Jul/19 $$\mathrm{easier}\:\mathrm{than}\:\mathrm{it}\:\mathrm{seems} \\ $$$$\left(\mathrm{1}\right)\:\:{x}+{y}+{z}=\mathrm{0}\:\Rightarrow\:{z}=−{x}−{y} \\ $$$$\mathrm{insert}\:\mathrm{this}\:\mathrm{in}\:\left(\mathrm{2}\right)\:\mathrm{and}\:\left(\mathrm{3}\right) \\ $$$$\left(\mathrm{2}\right)\:−\mathrm{3}{xy}\left({x}+{y}\right)=\mathrm{18} \\ $$$$\left(\mathrm{3}\right)\:\:−\mathrm{7}{xy}\left({x}+{y}\right)\left({x}^{\mathrm{2}}…

x-y-x-y-a-x-2-y-2-b-a-b-R-

Question Number 65054 by behi83417@gmail.com last updated on 24/Jul/19 $$\begin{cases}{\sqrt{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}}+\sqrt{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{y}}}=\boldsymbol{\mathrm{a}}}\\{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\boldsymbol{\mathrm{b}}\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\boldsymbol{\mathrm{R}}\right]}\end{cases} \\ $$ Commented by behi83417@gmail.com last updated on 24/Jul/19 $$\mathrm{thanks}\:\mathrm{in}\:\mathrm{advance}\:\mathrm{proph}.\:\mathrm{Abdo}. \\ $$$$\left[\boldsymbol{\mathrm{u}}+\boldsymbol{\mathrm{v}}=\boldsymbol{\mathrm{a}}\Rightarrow\boldsymbol{\mathrm{u}}^{\mathrm{2}} +\boldsymbol{\mathrm{v}}^{\mathrm{2}}…

d-dx-x-

Question Number 130496 by Adel last updated on 26/Jan/21 $$\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}!\right)=? \\ $$ Answered by MJS_new last updated on 26/Jan/21 $${x}!\:\mathrm{is}\:\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{N}\:\Rightarrow\:\mathrm{no}\:\mathrm{derivate}\:\mathrm{exists} \\ $$$$ \\ $$$$\mathrm{if}\:\mathrm{you}\:\mathrm{mean}\:{x}!=\Gamma\:\left({x}+\mathrm{1}\right) \\…

Question-130476

Question Number 130476 by shaker last updated on 26/Jan/21 Answered by TheSupreme last updated on 26/Jan/21 $$\left(\frac{\mathrm{3}}{\mathrm{5}}\right)^{{x}} +\left(\frac{\mathrm{4}}{\mathrm{5}}\right)^{{x}} =\mathrm{1} \\ $$$${f}\left({x}\right)=\left(\frac{\mathrm{3}}{\mathrm{5}}\right)^{{x}} +\left(\frac{\mathrm{4}}{\mathrm{5}}\right)^{{x}} \\ $$$${f}'\left({x}\right)<\mathrm{0}\:\forall{x}\in\mathbb{R} \\…