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Suppose $x^2+y^2+z^2+xyz=4$ with $-2\le x, y, z\le2$.

How can I get maximum of $${z(xy+xz+y)\over xy+y^2+z^2+1}$$

My attemt was to change $x, y, z$ to $2cosA, 2cosB, 2cosC$ with $A+B+C=\pi$. But it is not easy to take maximum of given form.

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  • $\begingroup$ Are you sure that we can write $2.27882...$ in a nice form? $\endgroup$ – Michael Rozenberg Nov 15 '19 at 5:07
  • $\begingroup$ what is the source of this problem? $\endgroup$ – ONG SEE HAI HCI Nov 15 '19 at 23:37

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