Ta có :
$x^{2018}+y^{2018}+z^{2018}=(xy)^{1009}+(yz)^{1009}+(zx)^{1009}$
$\to x^{1009}.(x^{1009}-y^{1009})+y^{1009}.(y^{1009}-z^{1009})+z^{1009}.(z^{1009}-x^{1009})=0$
$\to x=y=z$
Ta có :
$M = \bigg(\dfrac{x+y-z}{z}\bigg)^{2019}+\bigg(\dfrac{x-y+z}{y}\bigg)^{2019}+\bigg(\dfrac{z+y-x}{x}\bigg)^{2019} $
$ = 1+1+1=3$