- #1
tomwilliam2
- 117
- 2
I'm trying to do some practice Putnam questions, and I'm stuck on the following:
For ##a,b,c \geq 0##, prove that ##(a+b)(b+c)(c+a) \geq 8abc##
(https://www.math.nyu.edu/~bellova/putnam/putnam09_6.pdf)
I started off by expanding the brackets and doing some algebraic rearranging, but I don't think I've got anywhere.
Should I be using induction? Or is this an algebraic problem?
Thanks in advance
For ##a,b,c \geq 0##, prove that ##(a+b)(b+c)(c+a) \geq 8abc##
(https://www.math.nyu.edu/~bellova/putnam/putnam09_6.pdf)
I started off by expanding the brackets and doing some algebraic rearranging, but I don't think I've got anywhere.
Should I be using induction? Or is this an algebraic problem?
Thanks in advance