wrusb's blog

[Not relevant to CP] How difficult do you think this problem is?
By wrusb, 3 hours ago, In English

Problem. Consider real numbers $$$x, y, z$$$ satisfying $$$x^2 + y^2 + z^2 - \frac{1}{9}xy = 3$$$ and $$$xy + yz + zx \ge 0$$$. Find the minimum value of the expression:

$$$P = \frac{2}{3}(x^2 + y^2) + \frac{3}{4}z^2 + xy - \sqrt{12(xy + yz + zx)}$$$

Feel free to share your solutions and thoughts in the comments.

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