a,b,c成等比数列,a,x,b成等差数列,b,y,c成等差数列
则b^2=ac,2x=a+b,2y=b+c
所以a/x+c/y
=2a/2x+2c/2y
=2a/(a+b)+2c/(b+c)
=[2a(b+c)+2c(a+b)]/[(a+b)(b+c)]
=2[ab+ac+ac+bc]/[ab+ac+b^2+bc]
=2[ab+ac+ac+bc]/[ab+ac+ac+bc]
=2
a,b,c成等比数列,a,x,b成等差数列,b,y,c成等差数列
则b^2=ac,2x=a+b,2y=b+c
所以a/x+c/y
=2a/2x+2c/2y
=2a/(a+b)+2c/(b+c)
=[2a(b+c)+2c(a+b)]/[(a+b)(b+c)]
=2[ab+ac+ac+bc]/[ab+ac+b^2+bc]
=2[ab+ac+ac+bc]/[ab+ac+ac+bc]
=2