$a,b,c$ are positive real numbers which satisfy $5abc>a^3+b^3+c^3$. Prove that $a,b,c$ can form a triangle.
Problem
Source: Czech and Slovak Match 2000 P1
Tags: geometry, Geometric Inequalities, inequalities, algebra
Source: Czech and Slovak Match 2000 P1
Tags: geometry, Geometric Inequalities, inequalities, algebra
$a,b,c$ are positive real numbers which satisfy $5abc>a^3+b^3+c^3$. Prove that $a,b,c$ can form a triangle.