Problem

Source:

Tags: inequalities, inequalities proposed



Find the greatest value of the expression \[ \frac{1}{x^2-4x+9}+\frac{1}{y^2-4y+9}+\frac{1}{z^2-4z+9} \] where $x$, $y$, $z$ are nonnegative real numbers such that $x+y+z=1$.