You are Here: Home >< Maths

# Ukmt senior maths mentoring watch

1. Need help on this question (5b if you have the sheet):

Prove that for all positive real numbers, a,b and c that :

(a+b+c)/2
[is greater than or equal to]
(bc)/(b+c) + (ca)/(c+a) + (ab)/(a+b)
2. (Original post by pal04)
Need help on this question (5b if you have the sheet):

Prove that for all positive real numbers, a,b and c that :

(a+b+c)/2
[is greater than or equal to]
(bc)/(b+c) + (ca)/(c+a) + (ab)/(a+b)
Have you tried anything?
3. (Original post by RDKGames)
Have you tried anything?
I've tried taking the right from the left to hopefully be left with a positive remainder, but to make both of the denominators common and so on makes everything incredibly complicated which leads me to believe that it's not the best route to go

I've also considered drawing geometrical representations of each of the fractions but so far, nothing's coming to mind...
4. (Original post by pal04)
I've tried taking the right from the left to hopefully be left with a positive remainder, but to make both of the denominators common and so on makes everything incredibly complicated which leads me to believe that it's not the best route to go

I've also considered drawing geometrical representations of each of the fractions but so far, nothing's coming to mind...
Perhaps you can start out with the RHS, and assume WLOG that , then proceed to simplify bits and start using inequalities which you know are true to simplify the case down to the LHS.

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: October 31, 2017
Today on TSR

### The TSR A-level options discussion thread

Choosing A-levels is hard... we're here to help

### University open days

• Heriot-Watt University
School of Textiles and Design Undergraduate
Fri, 16 Nov '18
• University of Roehampton
Sat, 17 Nov '18
• Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 17 Nov '18
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