求教:四边形ABCD中,角A=角C=90度,DA=DC=1,延长AD,BC交于点P,则AB*S△ABP的最小值是多少?很着急

Question

求教:四边形ABCD中,角A=角C=90度,DA=DC=1,延长AD,BC交于点P,则AB*S△ABP的最小值是多少?很着急

Answer 1

设DP=x,PC=√(x^2-1).由△PDC∽△PBA,PC/PA=CD/AB,AB=(x+1)/√(x^2-1).AB*S△ABPAB*(AB*PA/2)=(1/2)*(x+1)^2/(x-1)=(1/2)*[x+3+4/(x-1)]=2+(1/2)*[(x-1)+4/(x-1)].中括号内两项的乘积一定,当两项相等时,两项的和最小...