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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?)

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?)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7.27. Let $1 = X + Y and 82 = XY be the elementary symmetric polynomials in R[X, Y], and for each d > 1, let Pa (X,Y)= Xd + yd. - 282, and p3= s³ -38182. (a) Prove that p₁ = 81, P2 =s (b) Prove by induction that Pa E R[81, 82] for all d > 1. (Hint. What does pa si look like?) -
Transcribed Image Text:7.27. Let $1 = X + Y and 82 = XY be the elementary symmetric polynomials in R[X, Y], and for each d > 1, let Pa (X,Y)= Xd + yd. - 282, and p3= s³ -38182. (a) Prove that p₁ = 81, P2 =s (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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