已知a+x^2=2003,b+x^2=2004,c+x^2=2005,且abc=6012.求a/bc + b/ac + c/ab- 1/a - 1/b - 1/c的值

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已知a+x^2=2003,b+x^2=2004,c+x^2=2005,且abc=6012.求a/bc + b/ac + c/ab- 1/a - 1/b - 1/c的值

已知a+x^2=2003,b+x^2=2004,c+x^2=2005,且abc=6012.求a/bc + b/ac + c/ab- 1/a - 1/b - 1/c的值
已知a+x^2=2003,b+x^2=2004,c+x^2=2005,且abc=6012.求a/bc + b/ac + c/ab- 1/a - 1/b - 1/c的值

已知a+x^2=2003,b+x^2=2004,c+x^2=2005,且abc=6012.求a/bc + b/ac + c/ab- 1/a - 1/b - 1/c的值
a/bc + b/ac + c/ab- 1/a - 1/b - 1/c
=(a^2+b^2+c^2-bc-ac-ab)/abc
=(2a^2+2b^2+2c^2-2bc-2ac-2ab)/2abc
=((a-b)^2+(b-c)^2+(a-c)^2)/2abc
因为a-b=-1;b-c=-;a-c=-2;abc=6012
所以原式=(1+1+2)/(2*6012)=1/3006