lean_workbook_plus_17443

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.\n\na) Prove the inequality for $k=1$ .\n\nb) Find the smallest value of $k$ such that the inequality holds for all triangles.