1. Proof this

If a, b and c are positive real numbers, prove that: bc(b+c) + ca(c+a) + ab(a+b) is more than or equal to 6abc

2. Originally Posted by cedricc
If a, b and c are positive real numbers, prove that: bc(b+c) + ca(c+a) + ab(a+b) is more than or equal to 6abc
Have you tried calculating it out?

3. The first step is to distribute the 6abc into the three terms on the left side. Consider that case where a>b>c. Create a new variable for a-b and a-c. Then you can simplify the proof using your initial assumption. Since the proof is symmetric in abc, solving for a>b>c is sufficient. Well you also need to consider equities, but that only makes the proof easier.

Let me know if that helps or you need a bit more guidance.