∵a+x²=2000，b+x²=2001，c+x²=2002，
∴b-a=1，c-b=1，c-a=2，
∵abc=24，
∴

a

bc

+

c

ab

+

b

ac

−

1

a

−

1

b

−

1

c

=

a2+ b2+c2−bc−ac−ab

abc

=

2a2+2b2+2c2−2bc−2ac−2ab

2abc

=

(a−b)2+(a−c)2+(b−c)2

2abc

=

1+4+1

2×24

=

1

8

．