x,a,y成等差数列,则2a=x+y,a=(x+y)/2.x,c,y成等比数列,则c^2=xy
a^2/c^2=[(x+y)/2]^2/(xy)=(x+y)^2/(4xy)
x>0,y>0,由均值不等式得(x+y)^2≥4xy
a^2/c^2≥(4xy)/(4xy)=1,a^2/c^2的最小值为1,此时x=y.