请教代学高手???

来源:百度知道 编辑:UC知道 时间:2024/05/27 23:37:19
已知:a+x^2=2004;b+x^2=2005;c+x^2=2006,且abc=24.求a/bc+b/ac+c/ab-1/a-1/b-1/c的值.

不难看出a,b,c是以1为等差的等差数列,且a>b>c
又因为abc=24
可知a=2,b=3,c=4
所以答案为1/8

a/bc+b/ac+c/ab-1/a-1/b-1/c

=a/bc+b/ac+c/ab-b/ab-c/bc-a/ac

=(a/bc-c/bc)+(b/ac-a/ac)+(c/ab-b/ab)

=(a-c)/bc+(b-a)/ac+(c-b)/ab

=(a-c+x^2-x^2)/bc+(b-a+x^2-x^2)/ac+(c-b+x^2-x^2)/ab

=(a+x^2-c-x^2)/bc+(b+x^2-a-x^2)/ac+(c+x^2-b-x^2)/ab

=((a+x^2)-(c+x^2))/bc+((b+x^2)-(a+x^2))/ac+((c+x^2)-(b+x^2))/ab

=(2004-2006)/bc+(2005-2004)/ac+(2006-2005)/ab

=-2/bc+1/ac+1/ab

=-2a/abc+b/abc+c/abc

=(-2a+b+c)/abc

=(-a-a+b+c)/abc

=((b-a)+(c-a))/abc

=((b-a+x^2-x^2)+(c-a+x^2-x^2))/abc

=((b+x^2-a-x^2)+(c+x^2-a-x^2))/abc

=(((b+x^2)-(a+x^2))+((c+x^2)-(a+x^2)))/abc

=((2005-2004)+(2006-2004))/24

=(1+2)/24

=3/24

=1/8