已知b²=ac,x=c+b/2,y=c+b/2,求证:a/x+c/y=2

已知b²=ac,x=c+b/2,y=c+b/2,求证:a/x+c/y=2
已知b²=ac,x=c+b/2,y=c+b/2,求证:a/x+c/y=2

已知b²=ac,x=c+b/2,y=c+b/2,求证:a/x+c/y=2
已知b²=ac,x=(a+b)/2,y=(c+b)/2,求证:a/x+c/y=2
a/x+c/y
=2a/(a+b)+2c/(b+c)
=2[a(b+c)+c(a+b)]/(a+b)(b+c)
=2[ab+ac+ac+cb]/[ab+ac+b²+bc]
=2[ab+ac+ac+bc]/[ab+ac+ac+bc]
=2