SMO Open · 4. Inequalities, extreme values and the integer part
Bound with AM-GM or Cauchy–Schwarz, read square roots as distances, trap the integer part between two integers, and always check when equality holds.
Use AM-GM (including weighted splits) and Cauchy–Schwarz, and check that equality is attainable.
Translate square roots, circles and slopes into distances and tangents.
Work with the integer part by trapping between consecutive integers and counting blocks.
Write a complete Round 2 inequality proof with correct strict signs.