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(a + b)/c +(b + c)/a +(c + a)/b >= a + b + c +1/a+1/b+1/c

Source: 2016 Saudi Arabia Pre-TST Level 4+ 1.2

September 13, 2020

algebrainequalities

Problem Statement

Let

a, b, c

be positive numbers such that

a^2+b^2+c^2+abc = 4

. Prove that

\frac{a + b}{c} +\frac{b + c}{a} +\frac{c + a}{b} \ge a + b + c + \frac{1}{a} + \frac{1}{b} +\frac{1}{c}