Solve Hard Inequalities Like a Pro (AM-GM Explained)

🔥 Want to solve Math Olympiad problems faster? In this video, I explain and prove the QM-AM-GM-HM inequalities step by step, and show you how to use the AM-GM inequality to solve two challenging Olympiad-style problems. 📚 What you’ll learn in this video: ✅ The definitions of Quadratic Mean (QM), Arithmetic Mean (AM), Geometric Mean (GM), and Harmonic Mean (HM) ✅ How to prove the AM ≥ GM inequality and understand why it works ✅ Two real Math Olympiad problems solved using AM-GM inequality ✅ Tricks to recognize when to use inequalities in problem solving 🎯 If you’re preparing for IMO, AIME, USAMO, or any math competition, this inequality trick will make solving hard problems much easier. 👉 Don’t forget to like, subscribe, and comment if this helped you! 0:00 - Proof for Two variables 4:44 - Examples of n variables 8:32 - Problem 1 16:02 - Problem 2 (IMO 1995!!!)