=xyz,求x^2+y^2+z^2/xyz的最小值

网友回答

化成齐次式((x^2+y^2+z^2)/xyz)^2 >= (xx+yy+zz)^2 /((x+y+z)xyz)
xx+yy+zz>=1/3*(x+y+z)^2
x+y+z >= 3(xyz)^(1/3)
xx+yy+zz >= 3(xyz)^(2/3)
三式相乘：(xx+yy+zz)^2 >= 3(x+y+z)xyz
=>((x^2+y^2+z^2)/xyz)^2 >=3=>(x^2+y^2+z^2)/xyz >= 3^(1/2）