Ta có: [tex]\frac{x^2}{y+z}+\frac{y^2}{x+z}+\frac{z^2}{x+y}=x(\frac{x}{y+z}+1-1)+y(\frac{y}{x+z}+1-1)+z(\frac{z}{x+y}+1-1)=x(\frac{x+y+z}{y+z}-1)+y(\frac{x+y+z}{x+z}-1)+z(\frac{x+y+z}{x+y}-1)=(x+y+z)(\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{x+y})-(x+y+z)=0\Rightarrow M=2019[/tex]