70 lines
1.4 KiB
TeX
70 lines
1.4 KiB
TeX
\documentclass[a4paper,10pt]{article}
|
|
\RequirePackage[utf8x]{inputenc}
|
|
\RequirePackage[francais]{babel}
|
|
\RequirePackage{amssymb}
|
|
\RequirePackage{amsmath}
|
|
\RequirePackage{amsfonts}
|
|
\RequirePackage{subfig}
|
|
\RequirePackage{graphicx}
|
|
\RequirePackage{color}
|
|
|
|
\Block{from "macros/poly2Deg.tex" import solveEquation}
|
|
|
|
% Title Page
|
|
\title{Calcul littéral et statistiques}
|
|
\date{\today}
|
|
|
|
\begin{document}
|
|
\maketitle
|
|
|
|
|
|
\section{Polynômes}
|
|
|
|
|
|
|
|
\Block{set P = Polynom_deg2.random(["{a}", "{b}", "{c}"], ["{b}**2 - 4*{a}*{c} == 0"])}
|
|
Résoudre l'équation suivante
|
|
\begin{eqnarray*}
|
|
\Var{P} & = & 0
|
|
\end{eqnarray*}
|
|
|
|
Solution:
|
|
|
|
\Var{solveEquation(P)}
|
|
|
|
\bigskip
|
|
~\dotfill
|
|
\bigskip
|
|
|
|
|
|
\Block{set P = Polynom_deg2.random(["{a}", "{b}", "{c}"])}
|
|
\Block{set Q = Polynom_deg2.random(["{a}", "{b}", "{c}"])}
|
|
Résoudre l'équation suivante
|
|
\begin{eqnarray*}
|
|
\Var{P} & = & \Var{Q}
|
|
\end{eqnarray*}
|
|
|
|
Solution:
|
|
|
|
On commence par se ramener à une équation de la forme $ax^2+bx+c = 0$.
|
|
|
|
\Block{set R = P - Q}
|
|
|
|
\begin{align*}
|
|
& & \Var{P} = \Var{Q} \\
|
|
\Var{R.explain() | calculus(name = "", sep = "\\Leftrightarrow", end = "= 0")}
|
|
\end{align*}
|
|
|
|
On cherche maintenant à résoudre l'équation $\Var{R} = 0$.
|
|
|
|
\Var{solveEquation(R)}
|
|
|
|
\end{document}
|
|
|
|
%%% Local Variables:
|
|
%%% mode: latex
|
|
%%% TeX-master: "master"
|
|
%%% End:
|
|
|
|
|