化成((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）
故X^2+Y^2+Z^2+2/(XYZ)的最小值是√3.