1.

Prove that

$\displaystyle a^4 + b^4 + c^4 >= a^2bc+b^2ac+c^2ab$

holds for all real numbers a, b and c

(>= means greater than or equal to)

2.

Prove that if real numbers a, b and c satisfy

$\displaystyle a + b + c> 0 $

$\displaystyle ab +ac +bc > 0 $

$\displaystyle abc > 0$

then each of a, b, and c is positive

Thanks for the help guys ^_^