2016-2017/3e/DM/DM_17_05_10/dev_facto_eq.tex
2017-06-16 09:49:23 +03:00

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% theme: Calcul litteral
\begin{parts}
\part Développer les expressions suivantes
\begin{multicols}{3}
\begin{subparts}
\Block{set e = Expression.random("_*(_*x + _)")}
\subpart $A = \Var{e}$
\begin{solution}
\begin{eqnarray*}
\Var{e.simplify().explain() | calculus(name = "A")}
\end{eqnarray*}
\end{solution}
\Block{set e = Expression.random("(_*x+_)(_*x + _)", val_min = 2)}
\subpart $B = \Var{e}$
\begin{solution}
\begin{eqnarray*}
\Var{e.simplify().explain() | calculus(name = "B")}
\end{eqnarray*}
\end{solution}
\columnbreak
\Block{set e = Expression.random("(_*x + _)^2", val_min = 2)}
\subpart $C = \Var{e}$
\begin{solution}
\begin{eqnarray*}
\Var{e.simplify().explain() | calculus(name = "C")}
\end{eqnarray*}
\end{solution}
\end{subparts}
\end{multicols}
\part Factoriser les expressions suivantes
\begin{multicols}{3}
\begin{subparts}
\Block{set e = Expression.random("{a}x*(_*x + _)", conditions = ['{a} >= 2'])}
\subpart $A = \Var{e.simplify()}$
\begin{solution}
\begin{eqnarray*}
A = \Var{e.simplify()} = \Var{e}
\end{eqnarray*}
\end{solution}
\Block{set e = Expression.random("_x*(_*x + _)")}
\subpart $B = \Var{e.simplify()}$
\begin{solution}
\begin{eqnarray*}
B = \Var{e.simplify()} = \Var{e}
\end{eqnarray*}
\end{solution}
\columnbreak
\Block{set e = Expression.random("_x*(_*x + _)")}
\subpart $C = \Var{e.simplify()}$
\begin{solution}
\begin{eqnarray*}
C = \Var{e.simplify()} = \Var{e}
\end{eqnarray*}
\end{solution}
\end{subparts}
\end{multicols}
\part Résoudre les équations suivantes.
\begin{multicols}{3}
\begin{subparts}
\Block{set e = Equation.random("{a}x + _ = 0",
conditions = ["{a}!= 1"],
val_min = 2,
val_max = 150
)}
\subpart $\Var{e}$
\begin{solution}
\begin{align*}
\Block{for i in e.solve()} \Var{i[0]} &= \Var{i[1]} \\ \Block{endfor}
\end{align*}
\end{solution}
\Block{set e = Equation.random("_x + _ = _",
conditions = ["{a}!= 1"],
val_min = -10,
val_max = 15
)}
\subpart $\Var{e}$
\begin{solution}
\begin{align*}
\Block{for i in e.solve()} \Var{i[0]} &= \Var{i[1]} \\ \Block{endfor}
\end{align*}
\end{solution}
\Block{set e = Equation.random("{a}x + _ = {b}x + _",
conditions=["{a} != {b}"],
val_min = -10,
val_max = 20
)}
\subpart $\Var{e}$
\begin{solution}
\begin{align*}
\Block{for i in e.solve()} \Var{i[0]} &= \Var{i[1]} \\ \Block{endfor}
\end{align*}
\end{solution}
\end{subparts}
\end{multicols}
\end{parts}