parmenides51 wrote: Prove that for positive real numbers $a, b$ and $c$ the inequality $2(a^4+b^4+c^4) < (a^2+b^2+c^2)^2$ holds if and only if $a,b,c$ are the sides of a triangle. See also here https://artofproblemsolving.com/community/c6h561235p4863514