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Diffstat (limited to 'examples')
| -rw-r--r-- | examples/sample_data/1998-B-1.json | 12 |
1 files changed, 12 insertions, 0 deletions
diff --git a/examples/sample_data/1998-B-1.json b/examples/sample_data/1998-B-1.json new file mode 100644 index 0000000..4e9aa4b --- /dev/null +++ b/examples/sample_data/1998-B-1.json @@ -0,0 +1,12 @@ +{ + "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": {} +} |