Question

已知a分之1+b分之1=6分之1,b分之1+c分之1=9分之1,c分之1+a分之1=15分之1,求ab+bc+ca分之a

Answer 1

1/a+1/b=1/6,

1/b+1/c=1/9,

1/c+1/a=1/15,

三式相加,得,

2(1/a+1/b+1/c)=1/6+1/9+1/15,

所以1/a+1/b+1/c=31/180,

所以ab+bc+ca分之abc

=abc/(ab+bc+ac)

=1/(ab+bc+ca)÷abc

=1/(1/c+1/a+1/b)

=1/(31/180)

=180/31