问题 填空题
已知,
1
a
+
1
b
=
1
6
1
b
+
1
c
=
1
9
1
a
+
1
c
=
1
15
,则
abc
ab+bc+ac
=______.
答案

由已知得,

1
a
+
1
b
=
1
6
ac+bc
abc
=
1
6

1
b
+
1
c
=
1
9
ab+ac
abc
=
1
9

1
a
+
1
c
=
1
15
ab+bc
abc
=
1
15

2(ab+bc+ac)
abc
=
31
90

abc
ab+bc+ac
=
45
31

故答案为:

45
31

单项选择题
单项选择题