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(a + b)/(a^2 -ab + b^2) <= 4/ |a + b|

Source: 2008 Austria Beginners' Competition p3

October 12, 2022
inequalitiesalgebra

Problem Statement

Prove the inequality a+ba2−ab+b2≤4∣a+b∣\frac{a + b}{a^2 -ab + b^2} \le \frac{4}{ |a + b|} for all real numbers aa and bb with a+b≠0a + b\ne 0. When does equality hold?
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