Peux-tu démontrer cette inégalité ? (95% échouent, pourtant c'est simple)

Can you prove this algebraic inequality: ab/(a+b)b + bc/(b+c)c + ac/(a+c) ≤ (a+b+c)/2? In this video, I'll explain step-by-step the practical method for solving this type of classic but daunting exercise, typical of the second year of high school science. We'll cover: Why use the notable identities (a-b)² rather than (a+b)². How to manipulate fractions and inequalities without making sign errors. The generalization trick to save time in your proofs. Whether you're preparing for a test or simply enjoy a math challenge, this method will give you the tools to never get stuck on this kind of problem again. 💡 Tip: If you haven't seen my previous video on basic proof techniques, I recommend watching it right after this one to fully grasp the subject! Don't forget to subscribe to ludeduk-Academy so you don't miss any math lessons! 📍 Chapters Adding chapters helps viewers navigate and improves Google indexing. 00:00 Introduction and statement of the exercise 00:53 Why use this technique? (Analysis of the problem statement) 01:45 Choosing the notable identity: (a-b)² or (a+b)²? 03:06 Developing the first part of the inequality 06:10 Generalizing to the other terms (BC and AC) 07:12 Sum of the terms and final factorization 08:44 Conclusion and result of the proof Place this at the very end of your description. #Mathematics #SecondYearScience #Proof #Inequalities #Algebra #ludedukAcademy #MathRevision