a、b、c成等比数列,则b²=ac
x是a、b的等差中项,则2x=a+b x=(a+b)/2
y是b、c的等差中项,则2y=b+c y=(b+c)/2
a/x+ c/y
=(ay+cx)/(xy)
=[a(b+c)/2 +c(a+b)/2]/[(a+b)(b+c)/4]
=2(ab+2ac+bc)/(ab+ac+b²+bc)
=2(ab+2ac+bc)/(ab+2ac+bc)
=2