设1/(x+y)=a 1/(x+z)=b 1/(y+z)=c
则 a+c=5/6 (1)
b+c=7/12 (2)
a+b=3/4 (3)
(1)+(2)+(3) 2(a+b+c)=26/12 a+b+c=13/12 (4)
(4)-(1) b=1/4
(4)-(2) a=1
(4)-(3) c=1/3
所以 1/(x+y)=1 x+y=1 (5)
1/(x+z)=1/4 x+z=4 (6)
1/(y+z)=1/3 y+z=3 (7)
联立(5)(6)(7) 解得
x=1 y=0 z=3
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