当ab/a+b=3/2,bc/b+c=3,ac/a+c=999/1000.求abc/ab+bc+ca

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当ab/a+b=3/2,bc/b+c=3,ac/a+c=999/1000.求abc/ab+bc+ca当ab/a+b=3/2,bc/b+c=3,ac/a+c=999/1000.求abc/ab+bc+ca

当ab/a+b=3/2,bc/b+c=3,ac/a+c=999/1000.求abc/ab+bc+ca
当ab/a+b=3/2,bc/b+c=3,ac/a+c=999/1000.求abc/ab+bc+ca

当ab/a+b=3/2,bc/b+c=3,ac/a+c=999/1000.求abc/ab+bc+ca
ab/a+b=3/2
a+b/ab=2/3
1/a+1/b=2/3
同理
1/a+1/c=1000/999
1/b+1/c=1/3
2(1/a+1/b+1/c)=1999/999
(ab+ac+bc)/abc=1999/1998
abc/ab+bc+ca=1998/1999

由ab/a+b=3/2可得a+b/ab = 1/a + 1/b = 2/3
同理,1/b + 1/c = 1/3,1/a + 1/c = 1000/999,
三式相加得2*(1/a + 1/b + 1/c)= 1999/999,
所以1/a + 1/b + 1/c = 1999/1998
ab+bc+ca/abc = 1/a + 1/b + 1/c = 1999/1998
所以所求abc/ab+bc+ca = 1998/1999