Almost A Sphere, But Not Quite

Algebra Level 5

Let \(x,y,z\) be real numbers such that \(x^2+y^2+z^2+(x+y+z)^2=9\) and \(xyz\leq \frac{15}{32}\). To 2 decimal places, what is the greatest possible value of \(x\)?

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Calvin Lin by Calvin Lin
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