IMO 1983 LL GBR28
Show that if the sides a, b, c of a triangle satisfy the equation
IMO 1983 LL GBR28
Origin: GBR
Problem
Show that if the sides a, b, c of a triangle satisfy the equation 2(ab2 + bc2 + ca2) = a2b + b2c + c2a + 3abc, then the triangle is equilateral. Show also that the equation can be satisfied by positive real numbers that are not the sides of a triangle.