a) Let $a,b$ and $c$ be side lengths of a triangle with perimeter $4$. Show that $$a^2+b^2+c^2+abc<8.$$ b) Is there a real number $d<8$ such that for all triangles with perimeter $4$ we have a^2+b^2+c^2+abc$a,b$ and $c$ are the side lengths of the triangle?