Source Latex
sujet du devoir
\documentclass[12pt]{article}
%\usepackage{french}
\usepackage{amsfonts}\usepackage{amssymb}
\usepackage[french]{babel}
\usepackage{amsmath}
\usepackage[latin1]{inputenc}
\usepackage{a4wide}
\usepackage{graphicx}
\usepackage{epsf}
\usepackage{array}
\usepackage{color}
%\usepackage{pst-plot,pst-text,pst-tree}
% Raccourcis diverses:
\newcommand{\nwc}{\newcommand}
\nwc{\dsp}{\displaystyle}
\nwc{\ct}{\centerline}
\nwc{\bge}{\begin{equation}}\nwc{\ene}{\end{equation}}
\nwc{\bgar}{\begin{array}}\nwc{\enar}{\end{array}}
\nwc{\bgit}{\begin{itemize}}\nwc{\enit}{\end{itemize}}
\nwc{\la}{\left\{}\nwc{\ra}{\right\}}
\nwc{\lp}{\left(}\nwc{\rp}{\right)}
\nwc{\lb}{\left[}\nwc{\rb}{\right]}
\nwc{\bgsk}{\bigskip}
\nwc{\vsp}{\vspace{0.1cm}}
\nwc{\vspd}{\vspace{0.2cm}}
\nwc{\vspt}{\vspace{0.3cm}}
\nwc{\vspq}{\vspace{0.4cm}}
\def\N{{\rm I\kern-.1567em N}} % Doppel-N
\def\D{{\rm I\kern-.1567em D}} % Doppel-N
\def\No{\N_0} % Doppel-N unten 0
\def\R{{\rm I\kern-.1567em R}} % Doppel R
\def\C{{\rm C\kern-4.7pt % Doppel C
\vrule height 7.7pt width 0.4pt depth -0.5pt \phantom {.}}}
\def\Q{\mathbb{Q}}
\def\Z{{\sf Z\kern-4.5pt Z}} % Doppel Z
\nwc{\tm}{\times}
\nwc{\V}{\overrightarrow}
\nwc{\ul}[1]{\underline{#1}}
\newcounter{nex}[section]\setcounter{nex}{0}
\newenvironment{EX}{%
\stepcounter{nex}
\bgsk{\large {\bf Exercice }\arabic{nex}}\hspace{0.2cm}
}{}
\nwc{\bgex}{\begin{EX}}\nwc{\enex}{\end{EX}}
\nwc{\bgfg}{\begin{figure}}\nwc{\enfg}{\end{figure}}
\nwc{\epsx}{\epsfxsize}\nwc{\epsy}{\epsfysize}
\nwc{\bgmp}{\begin{minipage}}\nwc{\enmp}{\end{minipage}}
\textheight=25cm
\textwidth=18.5cm
\oddsidemargin=-1.4cm
\evensidemargin=0cm
\setlength{\unitlength}{1cm}
\def\euro{\mbox{\raisebox{.25ex}{{\it =}}\hspace{-.5em}{\sf C}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\thispagestyle{empty}
\vspace*{-2cm}
%\ul{Nom:}
\hspace{5cm}
{\Large Devoir � la maison}
\hfill $1^{\mbox{\scriptsize{�re}}}\,$S
\vspace{0.8cm}
\bgex
R�soudre les �quations ou in�quations : \vspd
\bgit
\item[a)] $2x^2-3x=x^2-2x+6$\vspd
\item[b)] $x^4+x^2-12=0$\vspd
\item[c)] $x^4-11x^2+28=0$\vspd
\item[d)] $\dsp2x-\frac{4}{x}-7=0$\vspd
\item[e)] $x^2-9x\geq 90$\vspd
\item[f)] $x^4+x^2-2<0$\vspd
\enit
{\it (Les �quations b), c) et f) sont dites �quations, ou
in�quations, bicarr�es)}.
\enex
%\vspd
%\bgex
%On consid�re le polyn�me du troisi�me degr� $P(x)=x^3+3x^2-4x-12$.
%\vspd
%\bgit
%\item[1)] Calculer $P(2)$. En d�duire une factorisation de $P$. \vspd
%\item[2)] D�terminer alors toutes les racines de $P$. \vspd
%\item[3)] R�soudre l'in�quation $P(x)\leq0$.
%\enit
%\enex
\vspd
\bgex
\bgit
\item[1)] D�terminer les solutions de l'�quation
$3x^3-7x^2-7x+3=0$.
(on pourra remarquer que $\alpha=-1$ est une racine du polyn�me du
troisi�me degr�). \vspd
\item[2)] On consid�re la fraction rationnelle :
$\dsp f(x)=\frac{3x^3-7x^2-7x+3}{3x^2-12x+12}$ \vspd
\bgit
\item[a)] D�terminer l'ensemble de d�finition de $f$. \vspd
\item[b)] R�soudre l'in�quation $f(x)\geq0$.
\enit
\enit
\enex
\end{document}
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