I've got stuck on this problem :
Let $a, b, c \geq 0$ such that $a ^ 2 + b ^ 2 + c ^ 2 = 12$. Prove that $(a+1)(b+1)(c+1) \leq 27$.
I've thought that mean inequality ($HM \leq GM \leq AM \leq PM$ - referring to harmonic, geometric, arithmetic and square mean) may help. I've also considered $CBS$ (Cauchy - Buniakowski - Scwarz) inequality and Cebîşev inequality, but I didn't get it right.
I would be thankful for some hints.