Inequality with 4 variables

Algebra Level 5

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

Let x,y,z,tx,y,z,t be positive real numbers satisfying x2+y2+z2+t2=10x^2+y^2+z^2+t^2=10 and xyzt=4xyzt=4.

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

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