Question 12
Suppose that $x,y,z$ are positive real numbers such that $$\frac{x^2}{x^2+1}+\frac{y^2}{y^2+1}+\frac{z^2}{z^2+1}=2.$$ If $m$ is the maximum value of $$\frac{x}{x^2+1}+\frac{y}{y^2+1}+\frac{z}{z^2+1},$$ find the value of $\lfloor m^2\rfloor$.