You are Here: Home >< Maths

Inequality watch

1. How can I show that for all positive integers a, b, and c, a/b + b/c + c/a >= 3?
2. (Original post by HapaxOromenon3)
How can I show that for all positive integers a, b, and c, a/b + b/c + c/a >= 3?
AM-GM inequality case n=3.

Posted from TSR Mobile
3. (Original post by physicsmaths)
AM-GM inequality case n=3.

Posted from TSR Mobile
Yes, that seems to work, with the list of integers being (ab^2, bc^2, ca^2). Thanks.
4. (Original post by HapaxOromenon3)
Yes, that seems to work, with the list of integers being (ab^2, bc^2, ca^2). Thanks.
You can do it directly.
Multiplying these terms gives 1 so LHS/3>=1 hence he inequality.
Alternatively note that a->ka b->kb etc the inequality is not changed so homegenous, so you may assume something which gives a different type of solution albeit longer but more satisfying.

Posted from TSR Mobile
5. The homogenous stuff is just food for thought for other inequalities where such a fact is very useful and used to the absolute extreme.

Posted from TSR Mobile

Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: July 17, 2016
Today on TSR

Exam Jam 2018

Join thousands of students this half term

Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants