325

Part of 1981 All Soviet Union Mathematical Olympiad

Problems(1)

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

Source:

a) Find the minimal value of the polynomial

P(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,y

polynomialminimumalgebrainequalities