如图如图
如图证明:x、y、z≥1,且1/x+1/y+1/z=2--->(x-1)/x+(y-1)/y+(z-1)/z=1,故依Cauchy不等式,得根(x+y+z)=根[(x+y+z)((x-1)/x+(y-1)/y+(z-1)/z)]>=根(x-1)+根(y-1)+根(z-1).