Let $a,b,c$ be three real positive(strictly) numbers. Prove that:
$(a^2+bc)(b^2+ca)(c^2+ab) \geq abc(a+b)(b+c)(c+a).$
I tried :
$abc\left(a+\frac{bc}{a}\right)\left(b+\frac{ca}{b}\right)\left(c+\frac{ab}{c}\right)\geq abc(a+b)(b+c)(c+a) $ and now I want to try to prove that for example $a+\frac{bc}{a} \geq a+b$
but I don't know if is is a good idea.
Thanks:)