已知a+x.x=2000,b+x.x=2001,c+x.x=2002,且abc＝24

题目

已知a+x.x=2000,b+x.x=2001,c+x.x=2002,且abc＝24
求a/bc+c/ab+b/ac-1/a-1/b-1/c的值

答案

由a+x^2=2000,b+x^2=2001,c+x^2=2002得:
a=2000-x^2
b=2001-x^2
c=2002-x^2
即:a,b,c是连续的3个自然数,又abc=24
所以:a=2
b=3
c=4
a/bc+c/ab+b/ac-1/a-1/b-1/c
=a^2/abc+c^2/abc+b^2/abc-1/a-1/b-1/c
=4/24+16/24+9/24-1/2-1/3-1/4
=1/6+2/3+3/8-1/2-1/3-1/4
=1/8