点P与点Q在线段AB上,且AP;PB=2;3,AQ;QB=3;4,PQ=3.求AB的长?

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点P与点Q在线段AB上,且AP;PB=2;3,AQ;QB=3;4,PQ=3.求AB的长?点P与点Q在线段AB上,且AP;PB=2;3,AQ;QB=3;4,PQ=3.求AB的长?点P与点Q在线段AB上,

点P与点Q在线段AB上,且AP;PB=2;3,AQ;QB=3;4,PQ=3.求AB的长?
点P与点Q在线段AB上,且AP;PB=2;3,AQ;QB=3;4,PQ=3.求AB的长?

点P与点Q在线段AB上,且AP;PB=2;3,AQ;QB=3;4,PQ=3.求AB的长?
∵AP:PB=2:3
∴设AP=2k PB=3k
同理设AQ=3m QB=4m
∵QB=PB-PQ
即4m=3k-3
又∵AP=AQ-PQ
即2k=3m-3
∵3m-3=2k
m-1=2/3k
m=2/3k+1
∵3k-3=4m
∴3k-3=8/3k+1
得k=12
AB=AP+PB
∴AB=2k+3k
AB=60

105

3/(3/7-2/5)=105