∴b-a=1，c-b=1，c-a=2，
原式=
| a2+b2+c2 |
| abc |
| 1 |
| a |
| 1 |
| b |
| 1 |
| c |
=
| a2+b2+c2 |
| abc |
| bc+ac+ab |
| abc |
=
| a2+b2+c2−bc−ac−ab |
| abc |
=
| a(a−c)+b(b−a)+c(c−b) |
| abc |
∵b-a=1，c-b=1，c-a=2，abc=6012，
∴原式=
| −2a+b+c |
| 6012 |
=
| −2a+a+1+c |
| 6012 |
=
| 1+c−a |
| 6012 |
=
| 1+2 |
| 6012 |
=
| 1 |
| 2004 |
| a |
| bc |
| b |
| ca |
| c |
| ab |
| 1 |
| a |
| 1 |
| b |
| 1 |
| c |
| a2+b2+c2 |
| abc |
| 1 |
| a |
| 1 |
| b |
| 1 |
| c |
| a2+b2+c2 |
| abc |
| bc+ac+ab |
| abc |
| a2+b2+c2−bc−ac−ab |
| abc |
| a(a−c)+b(b−a)+c(c−b) |
| abc |
| −2a+b+c |
| 6012 |
| −2a+a+1+c |
| 6012 |
| 1+c−a |
| 6012 |
| 1+2 |
| 6012 |
| 1 |
| 2004 |