代数式的求值

1.已知a.b.c.d为正整数，且b/a=(4d-7)/c,(b+1)/a=7(d-1)/c,则c/a的值为多少，则d/b的值为多少？

b/a = (4d-7)/c, b/(4d-7) = a/c,

(b+1)/a = 7(d-1)/c, (b+1)/[7(d-1)] = a/c.

b/(4d-7) = (b+1)/[7(d-1)],
7b(d-1) = (b+1)(4d-7),
7db - 7b = 4db + 4d - 7b - 7,
3db = 4d - 7,
d(4-3b) = 7.

d = 1, 4-3b =7.
或者d=7,4-3b = 1.
但4-3b =7, b = -1不符合b为正整数的要求。
因此，只有
d = 7, 4-3b = 1, b = 1.
此时，
c/a = 7(d-1)/(b+1) = 42/2 = 21,
d/b = 7/1 = 7.

2。已知abc=1,a+b+c=2,a^2+b^2+c^2=3,则1/(ab+c-1)+1/(bc+a-1)+1/(ac+b-1)的值为多少？

因 a+b+c=2,所以，
ab + c - 1 = ab + 1 - a - b = (a-1)(b-1)
bc + a - 1 = bc + 1 - b - c = (b-1)(c-1)
ac + b - 1 = ac + 1 - a - c = (a-1)(c-1)

1/(ab+c-1)+1/(bc+a-1)+1/(ac+b-1)
= 1/[(a-1)(b-1)] + 1/[(b-1)(c-1)] + 1/[(a-1)(c-1)]
= [c-1 + a-1 + b-1]/[(a-1)(b-1)(c-1)]
= [a+b+c-3]/[(a-1)(b-1)(c-1)]
= -1/[(a-1)(b-1)(c-1)]

而
ab + bc + ac = [(a+b