If the function f (x) = x2-4x + 3, the set M = {(x, y) | f (x) + F (y) ≤ 0}, and the set n = {(x, y) | f (x) - f (y) ≥ 0}, then the area of the region represented by the set M ∩ n in the plane rectangular coordinate system is______ ． | Math enthusiast | Mathematical art

If the function f (x) = x2-4x + 3, the set M = {(x, y) | f (x) + F (y) ≤ 0}, and the set n = {(x, y) | f (x) - f (y) ≥ 0}, then the area of the region represented by the set M ∩ n in the plane rectangular coordinate system is______ ．

Because f (x) = x2-4x + 3, f (y) = y2-4y + 3, then f (x) + F (y) = (X-2) 2 + (Y-2) 2-2, f (x) - f (y) = x2-y2-4 (X-Y) = (X-Y) (x + y-4).. P = {(x, y) | (X-2) 2 + (Y-2) 2 ≤ 2}, q = {(x, y) | (X-Y) (x + y-4) ≥ 0} π．

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