1/a+1/b=3,1/b+1/c=4,1/a+1/c=5,abc/ab+bc+ac=

问题描述:

1/a+1/b=3,1/b+1/c=4,1/a+1/c=5,abc/ab+bc+ac=

1/a+1/b=3,……(1)
1/b+1/c=4,……(2)
1/a+1/c=5……(3)
(1)+(2)+(3)得2(1/a+1/b+1/c)=12
1/a+1/b+1/c=6
∴abc/ab+bc+ac
=(abc÷abc)/[(ab+bc+ac)÷abc]
=1/[1/a+1/b+1/c]
=1/6