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maximize \frac{2x^{2}}{3x^{2}+y^{2}+2x(z+2)} + \frac{y+z}{x+y+z+2} - \frac{(x+y)^{2}+z^{2}}{16}, x \geq 0, y \geq 0, z \geq 0, 4(x^3+y^3)+z^3=2(x+y+z)(xy+yz-2)
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