A Plane, A Sphere And A Hyperbola Walked Into A Bar

Algebra Level 5

x,y,x, y, and zz are real numbers such that x+y+z=0 x+y+z= 0 and x2+y2+z2=1 x^2 + y^2 + z^2 = 1 . What is the smallest possible value of xyz xyz ?

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