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Algebra Level 5

{x2+y2=16z2+t2=25xtyz=20 \large \begin{cases} {x^2 + y^2 =16 } \\ {z^2 + t^2 = 25} \\ { xt - yz = 20} \end{cases}

If real numbers t,x,y,z t , x , y , z satisfy the system of equations above, find the maximum value of P=xz P = xz .

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