| (x−2)4+(x−1)2−1 |
| (x−1)(x−2) |
| (x−2)4+x(x−2) |
| (x−1)(x−2) |
=
| (x−2)3+x |
| x−1 |
=
| x3−6x2+12x−8+x |
| x−1 |
=
| x2(x−1)−5x(x−1)+8(x−1) |
| x−1 |
=x2-5x+8；
∵x2-5x-1991=0，
∴x2-5x=1991，
∴原式=1991+8=1999．
故选D．
| (x−2)4+(x−1)2−1 |
| (x−1)(x−2) |
| (x−2)4+(x−1)2−1 |
| (x−1)(x−2) |
| (x−2)4+x(x−2) |
| (x−1)(x−2) |
| (x−2)3+x |
| x−1 |
| x3−6x2+12x−8+x |
| x−1 |
| x2(x−1)−5x(x−1)+8(x−1) |
| x−1 |