方法①根据平均值不等式：x^2/(y+2z)+(y+2z)/9≥2√{[x^2/(y+2z)][(y+2z)/9]}=2x/3y^2/(z+2x)+(z+2x)/9≥2√{[y^2/(z+2x)][(z+2x)/9]}=2y/3z^2/(x+2y)+(x+2y)/9≥2√{[z^2/(x+2y)][(x+2y)/9]}=2z/3以上3式相加：x^2/...