Đáp án:
\[x^2-y=y^2-z\]
\[→x^2-y^2=y-z\]
\[→(x-y)(x+y)=y-z\]
\[→ x+y=\dfrac{y-z}{x-y}\]
\[→ x+y+1=\dfrac{y-z+x-y}{x-y}=\dfrac{x-z}{x-y}\]
CMTT: \[y^2-z=z^2-x\]
\[→y+z+1=\dfrac{y-x}{y-z}\]
\[x^2-y=z^2-x\]
\[→x+z+1=\dfrac{y-z}{x-z}\]
\[→ M = ( x+y+1)(y+z+1)(z+x+1)=\dfrac{x-z}{x-y}.\dfrac{y-x}{y-z}.\dfrac{y-z}{x-z}=-1\]
Vậy $M=-1$