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sum ab/(c-1) >= 12 if a,b,c>1

Source: 2024 Austrian Regional Competition For Advanced Students p1

March 26, 2024
inequalitiesalgebra

Problem Statement

Let aa, bb and cc be real numbers larger than 11. Prove the inequality abc−1+bca−1+cab−1≥12.\frac{ab}{c-1}+\frac{bc}{a - 1}+\frac{ca}{b -1} \ge 12. When does equality hold?
(Karl Czakler)
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