81 = X + Y and $2 = XY be the elementary symmetric polynomials in R[X, Y], and for each d > 1, let Pa(X,Y)= Xª+yd (a) Prove that p₁ = 81, p2 = s1 - 282, and p3 = s³ -38182. (b) Prove by induction that Pa E R[81, 82] for all d > 1. (Hint. What does pa - si look like?)

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