Question 143
The positive real numbers $x, y, z$ are such that $x + y + z = 4$ and
$x, y, z \in [0,2]$. Find the minimal value of the algebraic expression:
$$
A = \sqrt{2+x} + \sqrt{2+y} + \sqrt{2+z} + \sqrt{x+y} + \sqrt{y+z} + \sqrt{z+x}.
$$
$x, y, z \in [0,2]$. Find the minimal value of the algebraic expression:
$$
A = \sqrt{2+x} + \sqrt{2+y} + \sqrt{2+z} + \sqrt{x+y} + \sqrt{y+z} + \sqrt{z+x}.
$$