69 lines
3.4 KiB
TeX
69 lines
3.4 KiB
TeX
\begin{parts}
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\part Compléter les pointillés pour qu'il y est bien égalité.
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\hspace{-1cm}
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\begin{center}
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\Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
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$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\ldots}{\Var{c}}$
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\hfill
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\Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
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$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\ldots}{\Var{c}}$
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\hfill
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\Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
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$\dfrac{\cdots}{\Var{c}} = \dfrac{\Var{a}}{\Var{b}}$
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\hfill
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\Block{set a,b,c = random_str("{a},{b},{a*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
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$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\Var{c}}{\cdots}$
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\end{center}
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\vfill
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\part Faire les calculs suivants en détaillant les étapes (penser à simplifier les fractions quand c'est possible).
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\begin{multicols}{2}
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\begin{subparts}
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\Block{set e = Expression.random("{a} / {b} + {c} / {b}", ["{b} > 1", "{a} > 0", "{c} > 0"])}
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\subpart $A = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "A")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} + {c} / {b}", ["{b} > 1"])}
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\subpart $B = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "B")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} + {c} / {d*b}", ["{b} > 1", "{c} > 1", "{d} > 1"])}
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\subpart $C = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "C")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} + {c} / {d*b}", ["{b} > 1", "{d} > 1"])}
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\subpart $D = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "D")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} * {c}", ["{b} > 1", "{a} > 0", "{c} > 1", "{c} != {b}"])}
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\subpart $E = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "E")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} * {c} / {d}", ["{b} > 1", "{a} > 0", "{c} > 0", "{d} > 1"])}
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\subpart $F = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "F")}
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\end{eqnarray*}
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\end{solution}
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\end{subparts}
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\end{multicols}
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\end{parts}
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