(根号3,+1)的2001次方减去2倍的(根号3,+1)的2000次方减去2倍的(根号3,+1)的1999次方,加200

(sqrt(3)+1)^2001-2(sqrt(3)+1)^2000-2(sqrt(3)+1)^1999+2001
=[(sqrt(3)+1)^2-2(sqrt(3)+1)-2](sqrt(3)+1)^1999+2001
=[3+1+2sqrt(3)-2sqrt(3)-2-2](sqrt(3)+1)^1999+2001
=0(sqrt(3)+1)^1999+2001
=0+2001
=2001