x^3+y^3+z^3大于等于3XYZ还有x+y+z大于等于3倍的3次根号下xyz

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x^3+y^3+z^3大于等于3XYZ还有x+y+z大于等于3倍的3次根号下xyz
x^3+y^3+z^3大于等于3XYZ
还有x+y+z大于等于3倍的3次根号下xyz

x^3+y^3+z^3大于等于3XYZ还有x+y+z大于等于3倍的3次根号下xyz
x^3+y^3+z^3-3xyz
=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)
=(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]/2
≥0
x^3+y^3+z^3≥3xyz
设,a=x^3,b=y^3,c=z^3
代人上式有:
a+b+c大于等于3倍的3次根号下abc