2(x+1/x)=2(x²+1)/x,
因为(x-1)²>=0,
x²-2x+1>=0,
x²+1>=2x,
x>0,
(x²+1)/x>=2,
x=1时,(x²+1)/x有最小值.所以X=1时周长2(x+1/x)最小.