Will triangle inequality work ?

Algebra Level 4

Find the minimum real number \(k\) such that

\((x+y+z)^{2}(xy +yz +zx)^{2}≤k(x^2+xy +y^2)(y^2+yz+z^2)(z^2+zx+x^2)\) where \(x,y,z\) are positive real numbers.

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