Are there any restrictions on a,b and c?
i.e.
The question states this:
bc(b+c) + ca(c+a) + ab(a+b) > (or equal to) 6abc
These type of question are quite hard for me, as i do not know how to approach it. In easier variations, such as a^2+b^2 >= 2ab, it is easily recognizable. But not so with these questions
If anyone could enlighten me on their process of thought, along with solution, it would be very appreciated.
Ok thxs.
Just with the solutions Also sprach Zarathustra; did you just know the identity in the first line from experience? And also, to prove the first line, i found a solution, that followed your method. But in the given question
"bc(b+c) + ca(c+a) + ab(a+b) > (or equal to) 6abc",
is actually the first part, then followed few questions later by (a+b)(b+c)(a+c) >= 8abc. So im am wondering if there is another way to prove the original question?
And to pickslides; im not sure if thats the conditions since the question dosent present it. However, think you and Also sprach Zarathustra are right and that would be the conditions of the a,b,c.
EDIT:
perhaps using a^2+b^2 >= 2ab as hinted by question.