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If x, y, z are distinct positive real numbers the $$(x^2(y+z) + y^2(x+z) + z^2(x+y))/xyz$$ would always be
For the given expression value of x,y,z are distinct positive integers . So the value of expression will always be greater than value when all the 3 variables are equal . substitute x=y=z we get minimum value of 6 .
$$(x^2(y+z) + y^2(x+z) + z^2(x+y))/xyz$$ = x/z + x/y + y/z + y/x + z/y + z/x
Applying AM greater than or equal to GM, we get minimum sum = 6
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