MathDB
Inequality

Source: Iranian TST 2018, first exam, day1, problem 2

April 7, 2018
inequalities

Problem Statement

Determine the least real number kk such that the inequality (2aa−b)2+(2bb−c)2+(2cc−a)2+k≥4(2aa−b+2bb−c+2cc−a)\left(\frac{2a}{a-b}\right)^2+\left(\frac{2b}{b-c}\right)^2+\left(\frac{2c}{c-a}\right)^2+k \geq 4\left(\frac{2a}{a-b}+\frac{2b}{b-c}+\frac{2c}{c-a}\right) holds for all real numbers a,b,ca,b,c.
Proposed by Mohammad Jafari
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