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Part of 2015 Turkey EGMO TST

Problems(1)

Coordinate Plane Algebra (Turkey EGMO TST 2015)

Source: (Turkey EGMO TST 2015)

8/5/2016
Let a≥b≥0a \ge b \ge 0 be real numbers. Find the area of the region defined as;
K={(x,y):x≥y≥0K=\{(x,y): x\ge y\ge0 and ∀n\forall n positive integers satisfy an+bn≥xn+yn}a^n+b^n\ge x^n+y^n\}
in the cordinate plane.
geometryanalytic geometry