iParcours 3ème Exercice 1 page 30

ex1p30.ipynb

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    "### Exercice 1 page 30\n",
    "\n",
    "On commence par coder les deux programmes de calcul. Il faut noter que le résultat du premier programme en fonction de x est l'équivalent de $(x - 3)²$.\n",
    "Celui du second est $x² + 3x + 7$."
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    "def progA(x):\n",
    "    return pow(x - 3, 2)\n",
    "\n",
    "def progB(x):\n",
    "    return pow(x, 2) + 3 * x + 7"
   ]
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   "source": [
    "progA(1) == 4"
   ]
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   "source": [
    "progB(-5)"
   ]
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    "On développe l'expression littérale correspondant au programme A.\n",
    "\n",
    "\\begin{align*}\n",
    "  A &= (x - 3)^2 \\\\\n",
    "    &= x^2 - 6x + 9\n",
    "\\end{align*}\n",
    "\n",
    "Trouver un nombre de départ pour lequel les deux programmes donnent le même résultat\n",
    "revient à résoudre :\n",
    "\n",
    "\\begin{align*}\n",
    "  x^2 - 6x + 9 &= x^2 + 3x + 7 \\\\\n",
    "  -6x - 3x &= 7 - 9 \\\\\n",
    "  -9x &= -2 \\\\\n",
    "  x &= \\frac{2}{9}\n",
    "\\end{align*}\n",
    "\n",
    "On peut vérifier que c'est effectivement le cas."
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   "source": [
    "from fractions import Fraction\n",
    "progA(Fraction(2, 9)) == progB(Fraction(2, 9))"
   ]
  }
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