Question Number 147254 by Ar Brandon last updated on 19/Jul/21 $$\left.\mathrm{Soient}\:\mathrm{a}\in\right]\mathrm{0},\:\mathrm{1}\left[\:\mathrm{et}\:\mathrm{b}\in\mathbb{R}.\:\mathrm{Soit}\:\mathrm{f}\:\mathrm{une}\:\mathrm{application}\:\mathrm{de}\:\mathbb{R}\:\mathrm{dans}\:\mathrm{lui}-\mathrm{m}\hat {\mathrm{e}me},\:\mathrm{de}\:\mathrm{classe}\:\mathrm{C}^{\mathrm{1}} ,\:\mathrm{telle}\:\mathrm{que}\:\mathrm{pour}\:\mathrm{tout}\:\mathrm{r}\acute {\mathrm{e}el}\right. \\ $$$$\mathrm{x},\:\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{ax}+\mathrm{b}. \\ $$$$ \\ $$$$\mathrm{1}.\:\:\mathrm{Montrer}\:\mathrm{que}\:\mathrm{pour}\:\mathrm{tout}\:\mathrm{r}\acute {\mathrm{e}el}\:\mathrm{x},\:\mathrm{f}\left(\mathrm{ax}+\mathrm{b}\right)=\mathrm{af}\left(\mathrm{x}\right)+\mathrm{b}.\:\mathrm{En}\:\mathrm{d}\acute {\mathrm{e}duire}\:\mathrm{que}\:\mathrm{pour}\:\mathrm{tout}\:\mathrm{r}\acute {\mathrm{e}el}\:\mathrm{x}, \\ $$$$\:\:\mathrm{f}\:'\left(\mathrm{ax}+\mathrm{b}\right)=\mathrm{f}\:'\left(\mathrm{x}\right).…
Question Number 81698 by peter frank last updated on 14/Feb/20 Commented by mr W last updated on 14/Feb/20 $${question}\:{is}\:{wrong}! \\ $$ Answered by mr W…
Question Number 81692 by Power last updated on 14/Feb/20 Commented by MJS last updated on 14/Feb/20 $$\mathrm{just}\:\mathrm{put}\:{a}=−{b}−{c} \\ $$$$\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\mathrm{9} \\ $$ Terms of Service Privacy…
Question Number 147231 by mathdanisur last updated on 19/Jul/21 $${if}\:\:\:\mathrm{3}^{\boldsymbol{{a}}+\mathrm{2}} \:=\:\mathrm{5}^{\mathrm{3}\boldsymbol{{b}}−\mathrm{1}} \:=\:\mathrm{7}^{\mathrm{3}−\mathrm{2}\boldsymbol{{c}}} \\ $$$${find}\:\:\:\boldsymbol{{a}}\centerdot\boldsymbol{{b}}\centerdot\boldsymbol{{c}}\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 19/Jul/21 $$\mathrm{3}^{{a}+\mathrm{2}} \:=\:\mathrm{5}^{\mathrm{3}{b}−\mathrm{1}}…
Question Number 147223 by mathlove last updated on 19/Jul/21 Commented by bramlexs22 last updated on 19/Jul/21 $$\:\:\:\mathrm{2}^{\mathrm{3x}} +\mathrm{2}^{\mathrm{x}} .\mathrm{3}^{\mathrm{2x}} −\mathrm{2}.\mathrm{3}^{\mathrm{3x}} \:=\:\mathrm{0} \\ $$$$\:\begin{cases}{\mathrm{2}^{\mathrm{x}} =\mathrm{u}}\\{\mathrm{3}^{\mathrm{x}} =\mathrm{v}}\end{cases}\:\Rightarrow\mathrm{u}^{\mathrm{3}}…
Question Number 81674 by Power last updated on 14/Feb/20 Commented by Tony Lin last updated on 14/Feb/20 $${let}\:{y}=\mathrm{7}−{x}^{\mathrm{2}} \\ $$$${x}+\left(\mathrm{7}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{11} \\ $$$${x}+\left({x}^{\mathrm{4}} −\mathrm{14}{x}^{\mathrm{2}}…
Question Number 81654 by peter frank last updated on 14/Feb/20 Commented by peter frank last updated on 14/Feb/20 $${we}\:{need}\:{to}\:{prove}\: \\ $$$${a}^{\mathrm{2}} {x}^{\mathrm{2}} +{b}^{\mathrm{2}} {y}={a}^{\mathrm{2}} \left({a}^{\mathrm{2}}…
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Question Number 147187 by mathdanisur last updated on 18/Jul/21 $${if}\:\:\left(\overline {{xyz}}\right)^{\mathrm{2}} \:=\:\left({x}+{y}+{z}\right)^{\mathrm{5}} \:\:{then}\:{find}: \\ $$$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} −\mid\left({x}+{y}+{z}\right)+\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)\mid \\ $$ Commented by…