Secrets in Inequalities

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Secrets in
(volume 1)

GIL Publishing House

© GIL Publishing House
Author: Pham Kim Hung

ISBN 978-973-9417-88-4
Copyright © 2007 by Gil. All rights reserved.

National Library of Romania CIP Description
Secrets in Inequalities (volume 1)
ISBN (13) 978-973-9417-88-4


Pham Kim Hung - zali!lu : Gil, 2007


GIL Publishing House
P.O. Box 44, Post Office 3, 450200, Zalau, Romania,
tel. (+4) 026.Q/616314
fax.: (+4) 0260/616414
e-mail: qiI1993@zalau.astral.ro


You are now keeping in your hands this new book of elementary inequalities. "Yet
another book of inequalities?" We hear you asking, and you may be right. Speaking
with the author's words:
" Myriads of inequalities and inequality techniques appear nowadays in books and
contests. Trying to learn all of them by heart is hopeless and useless. Alternatively, this
books objective is to help you understand how inequalities work and how you can set
up your own techniques on the spot, not just remember the ones you already learned.
To get such a pragmatic mastery of inequalities, you surely need a comprehensive
knowledge of basic inequalities at first. The goal of the first part of the book (chapters
1-8) is to lay down the foundations you will need in the second part (chapter g),
where solving problems will give you some practice. It is important to try and solve
the problems by yourself as hard as you can, since only practice will develop your
understanding, especially the problems in the second part. On that note, this books
objective is not to present beautiful solutions to the problems, but to present such a
variety of problems and techniques that will give you the best kind of practice."

It is true that there are very many books on inequalities and you have all the right
to be bored and tired of them. But we tell you that this is not the case with this one.
Just read the proof of Nesbitt's Inequality in the very beginning of the material, and
you will understand exactly what we mean.
Now that you read it you should trust us that you will find


this book new

and beautiful proofs for old inequalities and this alone can be a good reason to read
it, or even just to take a quick look at it. You will find a first chapter dedicated to
the classical inequalities: from AM-GM and Cauchy-Schwartz inequalities to the use
of derivatives, to Chebyshev'S and rearrangements' inequalities, you will find here
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