已知p:|1-(x-1)\3|小于等于2, q:x^2-2x+1-m^2小于等于0,(m>0),若ｐ是ｑ的充分不必要条件，求实数ｍ的范围,求过程1

已知p:|1-(x-1)\3|小于等于2, q:x^2-2x+1-m^2小于等于0,(m>0),若ｐ是ｑ的充分不必要条件，求实数ｍ的范围,求过程1

p:|1-(x-1)/3|=|(4-x)/3|<=2

∴|x-4|<=6

-6<=x-4<=6,即-2<=x<=10

q:x²-2x+1<=m²

∴(x-1)²<=m²

-m<=x-1<=m,即1-m<=x<=1+m

p是q的充分不必要条件,即-2<=x<=10在1-m<=x<=1+m上

1-m<=-2,1+m>=10

∴m>=9

综上,m范围为[9,+∞)