若a+x*x=1991 b+x*x=1992 c+x*x=1993 且abc=24 a/bc + b/ca + c/ab
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若a+x*x=1991 b+x*x=1992 c+x*x=1993 且abc=24 a/bc + b/ca + c/ab - 1/a - 1/b - 1/c 的值
![若a+x*x=1991 b+x*x=1992 c+x*x=1993 且abc=24 a/bc + b/ca + c/ab](/uploads/image/z/19515614-14-4.jpg?t=%E8%8B%A5a%2Bx%2Ax%3D1991+b%2Bx%2Ax%3D1992+c%2Bx%2Ax%3D1993+%E4%B8%94abc%3D24+a%2Fbc+%2B+b%2Fca+%2B+c%2Fab)
答案为1/8.
b-a=1,c-a=2,c-b=1.
a/bc + b/ca + c/ab - 1/a - 1/b - 1/c
=a/bc + b/ca + c/ab -b/ab-c/bc-a/ca
=a/bc-c/bc+b/ca-a/ca+c/ab-b/ab
=(a-c)/bc+(b-a)/ca+(c-b)/ab
=(a(a-c)+b(b-c)+c(c-b))/abc
=(-2a+b+c)/abc
=(b-a+c-a)/abc
=1/8
b-a=1,c-a=2,c-b=1.
a/bc + b/ca + c/ab - 1/a - 1/b - 1/c
=a/bc + b/ca + c/ab -b/ab-c/bc-a/ca
=a/bc-c/bc+b/ca-a/ca+c/ab-b/ab
=(a-c)/bc+(b-a)/ca+(c-b)/ab
=(a(a-c)+b(b-c)+c(c-b))/abc
=(-2a+b+c)/abc
=(b-a+c-a)/abc
=1/8
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