Maximizing the Almost Twin Expressions!

Algebra Level 5

\[\large{\dfrac{x}{1-yz} + \dfrac{y}{1-zx} + \dfrac{z}{1-xy} }\]

\[\large{\dfrac{x}{1+yz} + \dfrac{y}{1+zx} + \dfrac{z}{1+xy} }\]

Suppose that \(x,y,z \geq 0\) and \(x^2 + y^2 + z^2 = 1\). Let the maximum values of the expressions above be \(A\) and \(B\). Then find the value of \(\lfloor 100(A+B) \rfloor \).

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