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April 16, 2022 19:17
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iParcours 3e – Exercice 2 page 30
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"source": "### Exercice 2 page 30\n\nLes programmes qui correspondent aux deux programmes de calcul d'Alice sont :\n" | |
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"source": "def prog1(x):\n return pow(2 * x + 3, 2)\n\ndef prog2(x):\n return (pow(x, 2) * 4) + 12 * x + 9", | |
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"source": "En choisissant 3 comme nombre de départ, les deux programmes donnent\nle même résultat : 81" | |
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"source": "prog1(3) == prog2(3) == 81", | |
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"source": "Le premier programme est l'équivalent de $(2x + 3)^2$, \nle second de $4x^2 + 12x + 9$.\n\nTrouver le(s) nombre(s) choisi(s) par Alice ayant donné 9 comme résultat du deuxième\nprogramme revient à résoudre :\n\n\\begin{align*}\n4x^2 + 12x + 9 &= 9\\\\\n4x^2 + 12x &= 0\\\\\n4x(x + 3) &= 0\n\\end{align*}\n\nOr un produit de facteurs est nul si et seulement si un de ses facteurs au moins\nest nul.\n\nAinsi, on a :\n\\begin{align*}\n4x &= 0 \\qquad \\text{ou} \\qquad &x + 3 &= 0\\\\\n x &=0 &x &= -3\n\\end{align*}\n\nOn peut vérifier que ce sont les bonnes réponses." | |
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"source": "prog2(0) == prog2(-3) == 9", | |
"execution_count": 6, | |
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