# Help with inequalities

Though I know a few (Very few) Basic inequalities like the AM-GM-HM, RMS-AM-GM, etc., I feel that I am not able to use them properly with problems. Thus I would be very grateful if someone could suggest material online containing large number of examples which would help me get familiarized with solving inequalites.

Thanks!!

Note by Krishna Ar
4 years ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

Refer to the book $$\color{Red}{\text{Inequalities : An Approach Through Problems}}$$ , Written by $$\text{B. J. Venkatachala}$$. And if you like to read notes, you can find them in mine or @Dinesh Chavan 's feed.... Dinesh likes inequalities problems, and so do I (nowadays)!!!

Also, add the $$#inequalities$$ and All the hash tags related to inequalities like the " $$#AM-GM$$ , $$#AM-GMInequality$$ , $$#CauchySchwarzInequality$$, $$#Chebyshev'sInequality$$ " and all else.... If you want some problems and little bit theory of them, some notes are there in Dinesh Chavan's feed and I have also written one recently....

Here is the link of the book I mentioned (it's of amazon so costs 500 rupees), but you may try to search it for free at libgen.org. It's really helpful book, and when I had gone for the $$\text{INMOTC}$$ , they also told to refer this book .... (This statement was meant for underlining the importance of this book)

Inequalities

- 4 years ago

thanks ....... i'll try it too :)

- 3 years, 12 months ago

Thanks

- 2 years ago

Thanks for replying :D. I shall try to get that but I'd actually wanted to know of some online resource though! Talking about INMOTC-Can you tell how you actually did prepare for RMO? I see that you cleared it with distinction..so....

- 4 years ago

@Ashu Dablo : Congrats for winning Brainiac Delhi edition. Can you please help me out by telling me as to how the questions were, how to go about preparing? If you don't mind, could I have your email please?

- 3 years, 7 months ago

Thanks bro. Yeah, sure.

The id is thedashingboy.ashim@gmail.com

I know it sounds lame, but well, I was in class 3 when I made this.

@Krishna Ar you taking part in which edition??

- 3 years, 7 months ago

I'm taking part in the South edition (Chennai) on 10/1/15 :P. I have just sent you a mail , Do check it out. Thanks ^_^

- 3 years, 7 months ago

Search on google $$\text{ The Cauchy-Schwartz Master class}$$. This book is very helpful and contains a detailed explanation how to use and where to use the inequalities. Also it has very good problems. While searching on google just mention 'pdf' and you will get it. All the best.

- 3 years, 12 months ago

To save you some time, here's the book.

- 3 years, 12 months ago

Thanks for replying :). I actually found this quite tough after a few initial pages. Maybe I must come-back after reading a more elementary book. Tx again! :)

- 3 years, 12 months ago

thanks bro .. its really good :) ...... @Krishna Ar you should really try this. :)

- 3 years, 12 months ago

Yeah! Same problem here... These basic inequalies are not much comfortable!

- 3 years, 12 months ago

If you want online, http://www.artofproblemsolving.com/Wiki/index.php/Resourcesformathematics_competitions for more problem sets. Or maybe for more concept, http://yufeizhao.com/wc08/ineq.pdf or http://www.mathsolympiad.org.nz/wp-content/uploads/2008/12/inequalities.pdf. I hope it helps.

- 4 years ago

Thanks John for replying. But I guess you missed out a major point- Examples, right from simple to tough ones!!.

- 4 years ago

If you think that you really master, then attempt these...

- 4 years ago

I never said that I was a master!!! I actually meant that I wanted more examples :)

- 4 years ago

No.. what I mean is that to master more.. you answer the problems there..

- 3 years, 12 months ago

I have a PDF file by thomas mildorf ....... and it has all kinda problems from easy to really uncomfortable problems!! ............... I could send it if you drop in your e-mail ID in the comment box below :)

- 3 years, 12 months ago

Thanks for adding in :) I guess it was the same which Mathh had mentioned

- 3 years, 12 months ago

You probably mean this one.

- 3 years, 12 months ago

@Krishna Ar @mathh mathh ........ sorry guys thats the same one :p

- 3 years, 12 months ago

well, why don't you just search for them yourself? Here you can click on 'Inequalities Marathon' to find a lot of problems with solutions, you can also try 'Inequalities: A Mathematical Olympiad Approach', where in the pages 7-13 there are some AM-GM problems with solutions in the back of the book.

You can click on the next google page and click on 'Pham Kim Hung', a really great book ('Secrets in Inequalities'). Maybe 'Introduction to Inequalities' also. These are just random examples, there are so many pdf's on the google search, you can find some good ones there.

- 4 years ago

Chill please! I'm sorry if I'd unnecessarily tagged you in. Thanks

- 4 years ago

oh, sorry if I sounded rude, didn't mean to.

- 4 years ago

:) its ok

- 4 years ago