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ASU 325 All Soviet Union MO 1981 min of 4 +x^2y^4 + x^4y^2 - 3x^2y^2

Source:

July 23, 2019
polynomialminimumalgebrainequalities

Problem Statement

a) Find the minimal value of the polynomial P(x,y)=4+x2y4+x4y2āˆ’3x2y2P(x,y) = 4 + x^2y^4 + x^4y^2 - 3x^2y^2
b) Prove that it cannot be represented as a sum of the squares of some polynomials of x,yx,y.
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