Substitute Them Wisely

Algebra Level 3

{y+6=(x3)2x+6=(y3)2\large{ \begin{cases} y+6 = (x-3)^2 \\ x+6 = (y-3)^2 \end{cases}}

If xx and yy are distinct numbers that satisfy the system of equations above, find x2+y2x^2+y^2.

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