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   "source": [
    "# Chapter 6 : FORMULAE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 6_1 pgno:69"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "expr=8*i-5\n",
      "the number is  16\n"
     ]
    }
   ],
   "source": [
    " #8 times a number is decreased by 5 the result is 123\n",
    "#let x be the number\n",
    "\n",
    "print'expr=8*i-5'\n",
    "x=0;\n",
    "for x in range(0,100):\n",
    "  if((8*x-5)==123):\n",
    "    print\"the number is \",x\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 6_2 pgno:71"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "expr=(2*n+1)+(2*n+3)+(2*n+5)\n",
      "n=%i \n",
      "12\n",
      "\n",
      " the numbers are  199 201 203\n"
     ]
    }
   ],
   "source": [
    "#sum of 3 consecutive odd no.'s is 81\n",
    "\n",
    "#let the 3 consecutive odd numbers be 2n+1,2n+3,2n+5\n",
    "\n",
    "print\"expr=(2*n+1)+(2*n+3)+(2*n+5)\"\n",
    "n=0;\n",
    "for n in range(0,100):\n",
    "  if((2*n+1)+(2*n+3)+(2*n+5)==81):\n",
    "    print\"n=%i \\n\",n    \n",
    "\n",
    "n1=2*n+1;\n",
    "n2=2*n+3;\n",
    "n3=2*n+5;\n",
    "print\"\\n the numbers are \",n1,n2,n3\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 6_3 pgno:72"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p1=(6*x-5)\n",
      "p2=(2*x+9)\n",
      "p3=p1-p2\n",
      "satisfies the equation \n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "print\"p1=(6*x-5)\"\n",
    "p1=numpy.array([6, -5])\n",
    "print\"p2=(2*x+9)\"\n",
    "p2=numpy.array([2, 9])\n",
    "print\"p3=p1-p2\"\n",
    "p3=p1-p2\n",
    "\n",
    "x1=numpy.roots(p3)\n",
    "left=6*x1-5; #check by substituion \n",
    "right=2*x1+9;\n",
    "if(left==right):\n",
    "\tprint'satisfies the equation '\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 6_4 pgno:73"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x is a polynomial function\n",
      "by the law of sighs roots are [ 3.]\n"
     ]
    }
   ],
   "source": [
    "print\"x is a polynomial function\"\n",
    "import numpy\n",
    "p1=numpy.array([3/5+1/2, 0])\n",
    "p2=numpy.array([5/4, -3])\n",
    "#p1=3*x/5+x/2;\n",
    "#p2=5*x/4-3;\n",
    "p3=p1-p2;\n",
    "x=numpy.roots(p3) #by the law of signs\n",
    "print\"by the law of sighs roots are\",x\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 6_5 pgno:75"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p1=4*x-(x-2)/3\n",
      "p2=5+(2*x+1)/4\n",
      "p3=p1-p2\n",
      "satisfies the equation \n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "print\"p1=4*x-(x-2)/3\"\n",
    "p1=numpy.array([11/3, 2/3])\n",
    "print\"p2=5+(2*x+1)/4\"\n",
    "p2=numpy.array([1/2, 21/4])\n",
    "print\"p3=p1-p2\"\n",
    "p3=p1-p2\n",
    "\n",
    "x=numpy.roots(p3)\n",
    "left=4*x-(x-2)/3; #check by substituion \n",
    "right=5+(2*x+1)/4;\n",
    "if(left != right):\n",
    "\tprint'satisfies the equation '\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
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   "execution_count": null,
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   "source": []
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   "cell_type": "code",
   "execution_count": null,
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