# Maximizing given expression

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.

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