Problem

Source: Albanian BMO TST 2010 Question 4

Tags: inequalities, LaTeX, inequalities unsolved



Let's consider the inequality $ a^3+b^3+c^3<k(a+b+c)(ab+bc+ca)$ where $ a,b,c$ are the sides of a triangle and $ k$ a real number. a) Prove the inequality for $ k=1$. b) Find the smallest value of $ k$ such that the inequality holds for all triangles.