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\title{Développement (correspondance)}
\language{fr}
\range{-5..5}
\author{Odile Bénassy}
\email{obenassy@free.fr}
\computeanswer{no}
\format{html}
\precision{10000}

\integer{numexo=random(1,2)}
\integer{a1=random(2,3,4,5,6,7,8,9,10,12,15,20)}
\integer{b1=random(2,3,4,5,6,7,8,9,10,12,15,20)}
\integer{c1=random(2,3,4,5,6,7,8,9,10,12,15,20)}
\integer{d1=random(2,3,4,5,6,7,8,9,10,12,15,20)}
\text{s11=random(-,+)}
\text{s12=random(-,+)}
\text{s13=random(-,+)}
\text{s14=random(-,+)}
\integer{a2=\a1}
\integer{b2=\b1}
\integer{c2=\c1}
\integer{d2=\d1}
\text{s21=\s11}
\text{s22=\s12}
\if{\s13=+}{\text{s23=-}}{\text{s23=+}}
\text{s24=\s14}
\integer{a3=\a1}
\integer{b3=\b1}
\integer{c3=\c1}
\integer{d3=\d1}
\if{\s11=+}{\text{s31=-}}{\text{s31=+}}
\if{\s12=+}{\text{s32=-}}{\text{s32=+}}
\text{s33=\s13}
\text{s34=\s14}
\integer{a4=\a1}
\integer{b4=(\b1*2)}
\integer{c4=\c1}
\real{d4=\d1/2}
\text{s41=\s11}
\text{s42= \s12}
\text{s43=\s13}
\text{s44=\s14}
\integer{a5=\a1}
\real{b5=\b1/2}
\integer{c5=\c1}
\integer{d5=\d1*2}
\text{s51=\s11}
\text{s52= \s12}
\text{s53=\s13}
\text{s54=\s14}

\integer{res11 = (\s11 \a1) * (\s13 \c1)}
\integer{res12 = (\s11 \a1) * (\s14 \d1) + ((\s12 \b1) * (\s13 \c1))}
\integer{res13 = (\s12 \b1) * (\s14 \d1)}
\integer{res21 = (\s21 \a2) * (\s23 \c2)}
\integer{res22 = (\s21 \a2) * (\s24 \d2) + ((\s22 \b2) * (\s23 \c2))}
\integer{res23 = (\s22 \b2) * (\s24 \d2)}
\integer{res31 = (\s31 \a3) * (\s33 \c3)}
\integer{res32 = (\s31 \a3) * (\s34 \d3) + ((\s32 \b3) * (\s33 \c3))}
\integer{res33 = (\s32 \b3) * (\s34 \d3)}
\integer{res41 = (\s41 \a4) * (\s43 \c4)}
\integer{res42 = (\s41 \a4) * (\s44 \d4) + ((\s42 \b4) * (\s43 \c4))}
\integer{res43 = (\s42 \b4) * (\s44 \d4)}
\integer{res51 = (\s51 \a5) * (\s53 \c5)}
\integer{res52 = (\s51 \a5) * (\s54 \d5) + ((\s52 \b5) * (\s53 \c5))}
\integer{res53 = (\s52 \b5) * (\s54 \d5)}

\if{\s11=+}{\text{s11=}}
\if{\s21=+}{\text{s21=}}
\if{\s31=+}{\text{s31=}}
\if{\s41=+}{\text{s41=}}
\if{\s51=+}{\text{s51=}}
\if{\s13=+}{\text{s13=}}
\if{\s23=+}{\text{s23=}}
\if{\s33=+}{\text{s33=}}
\if{\s43=+}{\text{s43=}}
\if{\s53=+}{\text{s53=}}

\text{\factorisees = 
\((\s11 \a1 x \s12 \b1)(\s13 \c1 x \s14 \d1)),
\((\s21 \a2 x \s22 \b2)(\s23 \c2 x \s24 \d2)),
\((\s31 \a3 x \s32 \b3)(\s33 \c3 x \s34 \d3)),
\((\s41 \a4 x \s42 \b4)(\s43 \c4 x \s44 \d4)),
\((\s51 \a5 x \s52 \b5)(\s53 \c5 x \s54 \d5))
}

\text{\reduites = 
\(\res11 x^2 + \res12 x + \res13),
\(\res21 x^2 + \res22 x + \res23),
\(\res31 x^2 + \res32 x + \res33),
\(\res41 x^2 + \res42 x + \res43),
\(\res51 x^2 + \res52 x + \res53)
}

\text{range=shuffle(1,2,3,4,5)}
\text{firsts=\factorisees[\range]}
\text{seconds=\reduites[\range]}

\statement{

\if{debug iswordof \oefenv}{
<p>\factorisees
<p>\reduites
<p>\firsts
<p>\seconds
<p>\s11 et \s21
}
<p>Faire correspondre chaque expression littérale avec sa forme développée

<p><center>\embed{reply 1}</center>
}

\answer{Ma réponse :}{\firsts; \seconds}{type=correspond}