Not any old function. The original isWe are looking for a minimum (of a positive function).

[$]\sqrt[3]{\frac{x^3+y^3+z^3} {xyz}}+ \sqrt[2]{\frac{xy+yz+zx} {x^2 + y^2 + z^2}} \geq \sqrt[3]{3} + 1 [$]

which is not

[$] f(x, y, z) = \frac{x^2 + y^2 + z^2}{x y + y z + z x} [$]

The function has been inverted. Why? The problem has been changed.