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(a-b+c)(1/a -1/b +1/c ) >=1 if a >= b>= c > 0 2010 Saudi Arabia Pre-TST 3.1

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December 28, 2021
algebrainequalities

Problem Statement

Let a≥b≥c>0a \ge b \ge c > 0. Prove that (a−b+c)(1a−1b+1c)≥1(a-b+c)\left(\frac{1}{a}-\frac{1}{b}+\frac{1}{c}\right) \ge 1
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