y/(2-x*3^(1/2))+z/(2-y*3^(1/2))+x/(2-z*3^(1/2))
=y^2/(2y-xy*3^(1/2))+z^/(2z-yz*3^(1/2))+x^/(2x-zx*3^(1/2))
>=(x+y+z)^2/(2(x+y+z)-(xy+yz+zx)*3^(1/2)) (赫尔台不等式）
=(x+y+z)^2/(2(x+y+z)-3^(1/2))
>=3(xy+yz+zx)^2/(2(x+y+z)-3^(1/2))
=3/(2(x+y+z)-3^(1/2))
设x最大
x+y+z=(x^2+xy+xz)/x=(1-yz+x^2)/x>=1/x>=3^(1/2)
代入得y/(2-x*3^(1/2))+z/(2-y*3^(1/2))+x/(2-z*3^(1/2))>=3^(1/2)
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