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min of x^4 + y^4 - x^2y - xy^2 when x,y>0 and x + y <= 1

Source: Czech-Polish-Slovak Match Junior 2021, individual p4 CPSJ

September 12, 2021
algebrainequalities

Problem Statement

Find the smallest value that the expression takes x4+y4−x2y−xy2x^4 + y^4 - x^2y - xy^2, for positive numbers xx and yy satisfying x+y≤1x + y \le 1.
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