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\begin{document}

%%%%%%%%%%b{gedeonInfo}%%%%%%%%%
%%--Document N° 1316435489522--
%%--Equations et inéquations du second degré--
%%%%%%%%%%e{gedeonInfo}%%%%%%%%%


\begin{exercise}
Résoudre dans $%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
$ les équations suivantes:%
%TCIMACRO{\TeXButton{BeginMulticols}{\setlength{\columnseprule}{.2pt}
%\begin{multicols}{3}}}%
%BeginExpansion
\setlength{\columnseprule}{.2pt}
\begin{multicols}{3}%
%EndExpansion


\begin{enumerate}
\item
\[
3x^{2}-2=0;
\]


\item
\[
x^{2}+3x=0;
\]


\item
\[
-2x^{2}+3x+5=0;
\]


\item
\[
x^{2}-2\sqrt{2}x+2=0;
\]


\item
\[
\frac{x+3}{x-1}=\frac{2x-3}{x-2};
\]


\item
\[
x^{4}-5x^{2}+6=0.
\]

\end{enumerate}%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion

\end{exercise}

\begin{exercise}
Résoudre dans $%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
$ les inéquations suivantes (on pourra utiliser les résultats du I.):%
%TCIMACRO{\TeXButton{BeginMulticols}{\setlength{\columnseprule}{.2pt}
%\begin{multicols}{3}}}%
%BeginExpansion
\setlength{\columnseprule}{.2pt}
\begin{multicols}{3}%
%EndExpansion


\begin{enumerate}
\item
\[
3x^{2}-2\leq0;
\]


\item
\[
-2x^{2}+3x+5\leq0;
\]


\item
\[
\frac{x^{2}+3x}{-2x^{2}+3x+5}\geq0.
\]

\end{enumerate}%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion

\end{exercise}

\begin{exercise}
Factoriser, si possible, les polynômes suivants (on pourra utiliser les
résultats du I.):%
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%\begin{multicols}{3}}}%
%BeginExpansion
\setlength{\columnseprule}{.2pt}
\begin{multicols}{3}%
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\begin{enumerate}
\item
\[
P(x)=-2x^{2}+3x+5;
\]


\item
\[
Q(x)=x^{2}-2\sqrt{2}x+2;
\]


\item
\[
R(x)=2x^{2}+3x+5.
\]

\end{enumerate}%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion

\end{exercise}

\begin{exercise}
Résoudre dans $%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
^{2}$ le système:%
\[
\left\{
\begin{array}
[c]{c}%
xy=-1\\
x+y=5/6
\end{array}
\right.  .
\]

\end{exercise}

\begin{exercise}
On rappelle que la résistance équivalente $R$ à deux résistances $R_{1}$ et
$R_{2}$ branchées\linebreak en parallèle $%
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\qquad
\end{pmatrix}
$ est donnée par la relation:%
\[
R=\frac{R_{1}R_{2}}{R_{1}+R_{2}}.
\]


On dispose en parallèle deux résistors de résistance $R_{1}$ et $R_{2}%
=R_{1}+r$.

\begin{enumerate}
\item Ecrire la relation donnant $R$ en fonction de $R_{1}$ et $r;$

\item On prend $r=10\Omega$ et $R=5\Omega.$ Déterminer $R_{1}.$
\end{enumerate}
\end{exercise}


\end{document}