Minimising can be Difficult!

Algebra Level 5

For real numbers x,y,zx,y,z, subject to x+y+z>6x+y+z>6 and

x2+y2+z2xyz=(x+y)(y+z)(z+x)8(xy+yz+zx),x^2+y^2+z^2-xyz=(x+y)(y+z)(z+x)-8(xy+yz+zx),

what is the minimum value of xy+yz+zxxy+yz+zx?

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