# 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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