超级数学题└━━━━└━━└━━━━━┛APBQ如图,AB=1,点P、Q分别为线段AB的内分点和外分点,且AP/PB＝AQ/QB=X,求PQ的长.

Question

超级数学题
└━━━━└━━└━━━━━┛
A P B Q
如图,AB=1,点P、Q分别为线段AB的内分点和外分点,且AP/PB＝AQ/QB=X,求PQ的长.

Answer 1

AP/PB=X
则(1+X)PB=1,PB=1/(1+X)
AQ/QB=X
则（X-1）QB=1,QB=1/(X-1)
所以PQ=1/(X-1)+1/(X+1)=2X/(X^2-1)