Algebraic Inequality Product

Show that $(x^{2} y + y^{2} z + z^{2} x) (x y^{2} + y z^{2} + z x^{2}) > 9 x^{2} y^{2} z^{2}$ .

~10 minProof · checked by AIInequalitiesAM-GM inequality

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIX. Inequalities, Examples XIX.a, No. 7

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