點P與點Q在線段AB上,且AP:PB=3:2,AQ:QB=3:4,PQ=3,求線段AB的長?

點P與點Q在線段AB上,且AP:PB=3:2,AQ:QB=3:4,PQ=3,求線段AB的長?

設AQ=a PB=b
(a+3):b=3:2
3b=2a+6
a:(3+b)=3:4
4a=9+3b
3b=4a-9
所以
2a+6=4a-9
2a=15
a=15/2
b=7
線段AB的長為
15/2+3+7
=17.5