# 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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