已知a+x²=2003,b+x²=2004,c+x²=2005,且abc=6012,求a/bc+b/ca+c/ab-1/a-1/b-1/c的值
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![已知a+x²=2003,b+x²=2004,c+x²=2005,且abc=6012,求a/bc+b/ca+c/ab-1/a-1/b-1/c的值](/uploads/image/z/431692-52-2.jpg?t=%E5%B7%B2%E7%9F%A5a%2Bx%26sup2%3B%3D2003%2Cb%2Bx%26sup2%3B%3D2004%2Cc%2Bx%26sup2%3B%3D2005%2C%E4%B8%94abc%3D6012%2C%E6%B1%82a%2Fbc%2Bb%2Fca%2Bc%2Fab-1%2Fa-1%2Fb-1%2Fc%E7%9A%84%E5%80%BC)
已知a+x²=2003,b+x²=2004,c+x²=2005,且abc=6012,求a/bc+b/ca+c/ab-1/a-1/b-1/c的值
已知a+x²=2003,b+x²=2004,c+x²=2005,且abc=6012,求a/bc+b/ca+c/ab-1/a-1/b-1/c的值
已知a+x²=2003,b+x²=2004,c+x²=2005,且abc=6012,求a/bc+b/ca+c/ab-1/a-1/b-1/c的值
易知:b-a=1,c-b=1,c-a=2 .
a/bc+b/ca+c/ab-1/a-1/b-1/c
=(a/bc-1/a)+(b/ca-1/b)+(c/ab-1/c)
=(a^2-bc)/abc+(b^2-ac)/abc+(c^2-ab)/abc
=[(a^2-2ab+b^2)+(b^2-2bc+c^2)+(c^2-2ac+a^2)]/2*abc
=(1+1+4)/2*6012
=1/2004
∵a+x²=2003,b+x²=2004,c+x²=2005
∴a-b=-1 b-c=-1 c-a=2
a/bc+b/ac+c/ab-1/a-1/b-1/c
=(a/bc-1/a)+(1/ac-1/b)+1/ab-1/c)
=(a²-bc)/abc+(b²-ac)/abc+(c²-ab)/abc<...
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∵a+x²=2003,b+x²=2004,c+x²=2005
∴a-b=-1 b-c=-1 c-a=2
a/bc+b/ac+c/ab-1/a-1/b-1/c
=(a/bc-1/a)+(1/ac-1/b)+1/ab-1/c)
=(a²-bc)/abc+(b²-ac)/abc+(c²-ab)/abc
=(a²+b²+c²-ab-ac-bc)/abc
=[(a-b)²+(b-c)²+(c-a)²]/6012
=[(-1)²+(-1)²+2²]/6012
=4/6012
=1503
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