x^2+y^2+z^2>=3(∣xyz∣)^(2/3)将x^2+y^2+z^2=1代入得:3(∣xyz∣)^(2/3)=<1整理得:∣xyz∣<=(√3/3)^3当且仅当x=y=z=√3/3时成立,即:xyz最大值是√3/9
x^2+y^2+z^2>=3(∣xyz∣)^(2/3)∣xyz∣<=1/3√3,故xyz最大值是1/3√3
xyz<=x2+y2+z2/3=1/3
1/8
√3/9