#1674 · Algebra · Inequalities

Positivity of Symmetric Expressions

Show that the expressions $a (a - b) (a - c) + b (b - c) (b - a) + c (c - a) (c - b)$ and $a^{2} (a - b) (a - c) + b^{2} (b - c) (b - a) + c^{2} (c - a) (c - b)$ are both positive.

~15 minProof · checked by AIPolynomialsSymmetric polynomialsInequalities

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIX. Inequalities, Examples XIX.b, No. 14

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