{
  "index": "1998-B-1",
  "question": "Find the minimum value of\n\\[\n\\frac{(x+1/x)^6-(x^6+1/x^6)-2}{(x+1/x)^3+(x^3+1/x^3)}\n\\]\nfor $x>0$.",
  "solution": "Notice that\n\\[\n\\frac{(x+1/x)^6-(x^6+1/x^6)-2}{(x+1/x)^3+(x^3+1/x^3)}\n=(x+1/x)^3-(x^3+1/x^3)=3(x+1/x).\n\\]\nThe last expression has minimum value $6$ by AM-GM, achieved at $x=1$.",
  "vars": [
    "x"
  ],
  "params": [],
  "sci_consts": [],
  "problem_type": "calculation",
  "variants": {}
}