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Minimum value of x^5+y^5-x^4y-xy^4+x^2+4x+7 with x+y non-negative

Source: Cyprus 2022 Junior TST-1 Problem 3

February 21, 2022
algebrainequalities

Problem Statement

If x,yx,y are real numbers with x+y⩾0x+y\geqslant 0, determine the minimum value of the expression K=x5+y5−x4y−xy4+x2+4x+7K=x^5+y^5-x^4y-xy^4+x^2+4x+7 For which values of x,yx,y does KK take its minimum value?
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