Let
Then
and the inequality becomes
Now apply three times .
Alright, here goes.
Prove that
abc > (a+b-c)(a-b+c)(-a+b+c)
What I've done:
By AM>GM property,
(a+b+c)/3 > (abc)^(1/3)
By AM>GM property, I also found that
(a+b+c)/3 > ((a+b-c)(a-b+c)(-a+b+c))^(1/3)
From here onwards I'm stuck, since it doesn't really make sense now.
Need help here.
Thanks in advance.