O inegalitate draguta

[Doctor Gil]

Fie $a,b,c$ numere reale pozitive astfel incat $a^2+b^2+c^2+abc=4$. Aratati ca
$a+b+c+\frac{1}{4}min \{(a-b)^2, (b-c)^2, (c-a)^2 \}\leq3.$