Maximization with constraints

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 . The largest possible value of x2y2z2 x^2 y^2 z^2 can be expressed as ab \frac{a}{b}, where aa and bb are positive coprime integers. What is the value of a+ba+b?

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