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How to solve inequality, especially AM-GM?

Pardon me! I use a capital letter on my title since I'm very stressful with such thing. Anybody, how to solve the inequality using AM-GM-M or Cauchy Schwarz one, or something bla bla bla. Even I have read on wikis, I felt that why anyone can solve the problem but I don't. Anyone, tips maybe?

Thankies :)

Note by Figel Ilham
2 years, 10 months ago

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There is no "short-cut". Proving classical inequalities take a lot of work, to learn the various approaches of how to apply them. Read Applying the AM-GM Inequality to get a better sense of how to start, especially sections 1, 2, 3. In general, a lot of "skill and cunning" is involved, along with a healthy dose of creative ingenuity.

Staff - 2 years, 10 months ago

Thank you very much.. maybe that wiki will help me to solve my problem. Some of National Olympiad Science, Junior High School, takes a lot of work. Even days..

- 2 years, 10 months ago