#1899 · Algebra · Inequalities

An inequality with positive numbers

If $a, b, c$ are positive and the sum of any two greater than the third, prove that $(1 + \frac{b - c}{a})^{a} (1 + \frac{c - a}{b})^{b} (1 + \frac{a - b}{c})^{c} < 1$ .

~20 minProof · checked by AILogarithmic inequalitiesAM-GM inequality

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Miscellaneous Examples, No. 293

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