Inequality with 4 variables

Algebra Level 5

\[\large P=(x+y)(z+t)\]

Let \(x,y,z,t\) be positive real numbers satisfying \(x^2+y^2+z^2+t^2=10\) and \(xyzt=4\).

If the maximum value of the expression is \(S\), find \( \lfloor 100 S \rfloor \).

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