Алгебра 11 класс. Средние. Неравенства между средними. Профильный уровень

Want more additional materials on this topic? They're here: https://interneturok.ru/h/biblioteka/.... Interested in videos on other school topics? We'll be happy to see you here: https://interneturok.ru/kursy_i_uslug.... InternetUrok is an online school with a rich library of materials on all school subjects: video lessons, notes, tests and exercises, and prompt answers to your questions. And no ads! Different situations require the use of different averages. You're already familiar with the arithmetic mean and the geometric mean. In this lesson, we'll introduce the concepts of the root mean and harmonic mean and explore their application. We will also formulate and prove important theorems: the Cauchy-Bunyakovsky inequality and the Cauchy inequality on means. By studying their consequences, we will come to a surprising discovery: all the aforementioned means compare to each other in a specific way, regardless of the set of numbers. Contents: 0:00 - Introduction 0:12 - Mean Values 06:23 - The Cauchy-Bunyakovsky Inequality 10:41 - Consequences of the Cauchy-Bunyakovsky Inequality 14:39 - The Cauchy Inequality Additional Material: 21:42 - Proof of the Cauchy Inequality for Arbitrary n Watch other video lessons on algebra (effective course for 11th grade (advanced level)) in the playlist:    • Алгебра 11 класс. Эффективные курсы (профи...