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\renewcommand\thesubsubsection{\roman{subsection}. }


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\usepackage{CJK}
\newcommand\japonais[1]{\begin{CJK}{UTF8}{song}#1\end{CJK}}
\newcommand{\jzero}{\japonais{〇}}
\newcommand{\jun}{\japonais{一}}
\newcommand{\jdeux}{\japonais{二}}
\newcommand{\jtrois}{\japonais{三}}
\newcommand{\jquatre}{\japonais{四}}
\newcommand{\jcinq}{\japonais{五}}
\newcommand{\jsix}{\japonais{六}}
\newcommand{\jsept}{\japonais{七}}
\newcommand{\jhuit}{\japonais{八}}
\newcommand{\jneuf}{\japonais{九}}
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\newcommand{\jcentmillion}{\japonais{おく}}
\newcommand{\jgiga}{\japonais{ちょお}}





\usepackage{tabularx}

%%%%%%% Colonne épaisse
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                                 \hline
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%%%% enumerate sur n colonnes
\newenvironment{nliste}[2][{\bf 1.}]%
	{%\setlength{\multicolsep}{8pt}
           \setlength{\columnseprule}{0pt}
	 \begin{multicols}{#2}
	 \begin{enumerate}[#1]}%
	{\end{enumerate}
	 \end{multicols}}


\usepackage{sudoku}


\newcounter{num}
\renewcommand{\thenum}{\Roman{num}}
\newcommand\exot[2][\thenum]{\refstepcounter{num}
\vspace{0.5cm}
{\bfseries\large \textsf{Exercice #1\ \ #2}}\\ 
\par\nobreak 
\normalsize
\vspace{0.25cm}
}

\setdefaultenum{\bf 1.}{{\bf a.}}{\it i.}{}{}

%\entete{DS n°1}{Jeudi 4 octobre 2007}{Jean Perrin - T	extsuperscript{ale}S 5}%g,d,b


\lstset{numbers=none,language=XCAS,xleftmargin=10pt,%
keywordstyle =\color{red}\usefont{OT1}{cmtt}{b}{n},basicstyle=\ttfamily\footnotesize\color{red},commentstyle=\normalfont\scriptsize\slshape,breaklines=true,backgroundcolor=\color{0.9white}}


\newcommand{\MarqueCommandeGiac}[1]{%
    \color{red}$>\ $}
\newcommand{\MarqueLaTeXGiac}{%
    \color{blue}}
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%% On redéfinit l'allure des sections en gardant \section, etc.




\begin{document}
\setlength{\parindent}{0pt}
\pagestyle{empty}



%\psshadowbox*[fillcolor=0.8white,framearc=.25]{%

\fbox{
\begin{minipage}{\textwidth}
\smallskip
{\Large \bfseries \sffamily \begin{center} CORRIGÉ du Devoir Surveillé n°\jun \hfill Samedi $\maya{4}$ octobre $\maya{2008}$ \\
                                  \end{center}}
\smallskip
\end{minipage}
}


\vspace{1cm}




\exot[\jun]{(4 points)}

\begin{center} 
   \renewcommand*\arraystretch{1.5}
\begin{tabularx}{.9\linewidth}{Y{4}} 
   \whline 
   Nombre & $\mathbb{N}$ & $\mathbb{Z}$ &$\mathbb{D}$ & $\mathbb{Q}$ & $\mathbb{R}$ \\ 
   \whline 
   $\dfrac{63}{7}=9$ &$\in$ &$\in$ &$\in$ &$\in$ &$\in$ \\ 
   \hline 
   $\dfrac{23}{7} $&$\not\in$ & $\not\in$&$\not\in$ &$\in$ &$\in$ \\ 
   \hline 
   $-\dfrac{23}{25}=\frac{92}{100}$ &$\not\in$ & $\not\in$&$\in$ &$\in$ &$\in$ \\ 
   \hline 
   $5\sqrt{7}$ &$\not\in$ &$\not\in$ &$\not\in$ &$\not\in$ &$\in$ \\ 
   \hline 
   $-\sqrt{36}=-6$ &$\not\in$ &$\in$ &$\in$ & $\in$&$\in$ \\ 
   \hline 
   $\sqrt{9-4}=\sqrt{5} $&$\not\in$ &$\not\in$ &$\not\in$ &$\not\in$ &$\in$ \\ 
   \hline 
   $5 \times 10^3=\nombre{5000}$ &$\in$ &$\in$ &$\in$ &$\in$ &$\in$ \\ 
   \hline 
   $-2,4=\frac{-24}{10}$ &$\not\in$ &$\not\in$ &$\in$ &$\in$ &$\in$ \\ 
   \whline 
\end{tabularx} 
\end{center} 



\vspace{1cm}



\exot[\jdeux]{(3 points)}
Donnez :
   \begin{enumerate} 
   \addtolength\baselineskip{0.4cm}
      \item un nombre entier qui ne soit pas un nombre entier naturel : $-5$
      \item un nombre rationnel qui ne soit pas nombre décimal : $\frac{1}{3}$
      \item un nombre quelconque compris entre $0,1$ et $0,2$ : $0,11$
      \item un nombre réel qui ne soit pas un nombre rationnel : $\sqrt{2}$
      \item un nombre décimal compris entre $\dfrac{3}{2}$ et $\dfrac{5}{3}$ : $\frac{16}{10}$
      \item un nombre décimal strictement positif et inférieur à $10^{-2}$ : $\frac{1}{10^3}$   
   \end{enumerate}

\exot[\jtrois]{(4,5 points)}

%@Commande-1
\begin{lstlisting}
A:=2-(7/3)*(2/3)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ \frac{4}{9} \]}}

%@Commande-2
\begin{lstlisting}
B:=(42/45)/(35/18)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ \frac{12}{25} \]}}

%@Commande-3
\begin{lstlisting}
C:=(5^3*3*5^7)/(5^8*3^4)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ \frac{25}{27} \]}}

%@Commande-4
\begin{lstlisting}
E:=simplifier((sqrt(3)-2*sqrt(2))^2)
\end{lstlisting}
{\MarqueLaTeXGiac{\[\text{Psr 2, Mod 5.74456, Heu 1.6, Min1.6
GCD dim 1, n=20 maxpqdeg0 4(Vector [4])
// Using Heu gcd 
// mrref line 0}\]}}
{\MarqueLaTeXGiac{\[ -\left(4 \sqrt{6}\right)+11 \]}}

%@Commande-5
\begin{lstlisting}
D:=simplifier((sqrt(2)/sqrt(18))*9*sqrt(2))
\end{lstlisting}
{\MarqueLaTeXGiac{\[ 3 \sqrt{2} \]}}

%@Commande-6
\begin{lstlisting}
F:=simplifier(2*sqrt(50)+3*sqrt(18)-5*sqrt(72))
\end{lstlisting}
{\MarqueLaTeXGiac{\[ -\left(11 \sqrt{2}\right) \]}}


\exot[\jquatre]{(3 points)}

%@Commande-7
\begin{lstlisting}
ifactor(1940400)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ 2^{4} 3^{2} 5^{2} 7^{2}\cdot 11 \]}}

%@Commande-8
\begin{lstlisting}
simplifier(sqrt(1940400))
\end{lstlisting}
{\MarqueLaTeXGiac{\[ 420 \sqrt{11} \]}}

\exot[\jcinq]{(3 points)}


%@Commande-9
\begin{lstlisting}
A:=1/3/(1/3)*(4/7)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ \frac{4}{7} \]}}

%@Commande-10
\begin{lstlisting}
B:=(1+2/5)/(5/3-1/2)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ \frac{6}{5} \]}}



\exot[\jsix]{(3 points)}

%@Commande-11
\begin{lstlisting}
simplifier(3/(2-sqrt(5)))
\end{lstlisting}
{\MarqueLaTeXGiac{\[ -\left(3 \sqrt{5}\right)-6 \]}}

%@Commande-12
\begin{lstlisting}
simplifier((sqrt(7)-sqrt(2))/((sqrt(7)+sqrt(2))
\end{lstlisting}
{\MarqueLaTeXGiac{\[\text{Psr 2, Mod 5.74456, Heu 1.6, Min1.6
GCD dim 1, n=100 maxpqdeg0 4(Vector [4])
// Using Heu gcd 
// mrref line 0}\]}}
{\MarqueLaTeXGiac{\[ \frac{(-\left(2 \sqrt{14}\right)+9)}{5} \]}}

%@Commande-13
\begin{lstlisting}
simplifier((3*sqrt(2)-1)*(1+sqrt(2))-2*sqrt(2))
\end{lstlisting}
{\MarqueLaTeXGiac{\[ 5 \]}}

\exot[\jsept]{(2 points)}

%@Commande-14
\begin{lstlisting}
simplifier((3*sqrt(2)-1)*(1+sqrt(2))-2*sqrt(2))
\end{lstlisting}
{\MarqueLaTeXGiac{\[ 5 \]}}



\exot[\jhuit]{(2 points)}


%@Commande-15
\begin{lstlisting}
(3/4)^(-2)*(1/8)^5
\end{lstlisting}
{\MarqueLaTeXGiac{\[ \frac{1}{18432} \]}}

%@Commande-16
\begin{lstlisting}
ifactor(18432)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ 2^{11} 3^{2} \]}}




\exot[\jneuf]{(2 points)}

%@Commande-17
\begin{lstlisting}
((10^5)^4*(3*10^2)^(-2))/(1+3^2)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ \frac{1000000000000000}{9} \]}}



\exot[\jdix]{(3 points)}

%@Commande-18
\begin{lstlisting}
W:=1+sqrt(2)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ 1+\sqrt{2} \]}}

%@Commande-19
\begin{lstlisting}
simplifier(W^2)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ 2 \sqrt{2}+3 \]}}

%@Commande-20
\begin{lstlisting}
simplifier(W^3)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ 5 \sqrt{2}+7 \]}}

%@Commande-21
\begin{lstlisting}
simplifier(W^4)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ 12 \sqrt{2}+17 \]}}

%@Commande-22
\begin{lstlisting}
simplifier((a+b)^2)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ a^{2}+2 a b+b^{2} \]}}

%@Commande-23
\begin{lstlisting}
simplifier((a+b)^3)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ a^{3}+3 a^{2} b+3 a b^{2}+b^{3} \]}}

%@Commande-24
\begin{lstlisting}
simplifier((a+b)^4)
\end{lstlisting}
{\MarqueLaTeXGiac{\[ a^{4}+4 a^{3} b+6 a^{2} b^{2}+4 a b^{3}+b^{4} \]}}


%\end{multicols}
%\nettoyer

\end{document}

