ac/a+c=4,ab/a+b=5,cb/c+b=6 求a+b+c

题目

ac/a+c=4,ab/a+b=5,cb/c+b=6 求a+b+c

答案

ac/(a+c)=4,取倒数
(a+c)/ac=1/4
1/a+1/c=1/4.1
同理
1/a+1/b=1/5.2
1/b+1/c=1/6.3
1式+2式+3式得
2(1/a+1/b+1/c)=1/4+1/5+1/6
2(1/a+1/b+1/c)=15/60+12/60+10/60
1/a+1/b+1/c=37/120.4
将1式代入4式得
1/4+1/b=37/120
1/b=7/120
b=120/7
同理
c=120/13
a=120/17
a+b+c=120/7+120/13+120/17
=120(1/7+1/13+1/17)
=120(221/1547+119/1547+91/1547)
=120*431/1547
=51720/1547