Solve Hard Inequalities Like a Pro (AM-GM Explained)
Автор: Prime Time Mathematics
Загружено: 2025-07-30
Просмотров: 318
🔥 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!!!)
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