y=(3x²+2x+2)/(x²+x+1)
yx²+yx+y=3x²+2x+2
(y-3)x²+(y-2)x+(y-2)=0
x是实数,所以判别式大于等于0
(y-2)²-4(y-3)(y-2)>=0
(y-2)(y-2-4y+12)>=0
(y-2)(3y-10)<=0
2<=y<=10/3
所以原式最小是2
所以M<=2