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inequality with (not only) geometric solution

Source: II Caucasus Mathematical Olympiad

March 20, 2018
inequalities

Problem Statement

Given real numbers aa, bb, cc satisfy inequality ∣a2+b2−c2ab∣<2\left| \frac{a^2+b^2-c^2}{ab} \right|<2. Prove that they also satisfy equalities ∣b2+c2−a2bc∣<2\left| \frac{b^2+c^2-a^2}{bc} \right|<2 and ∣c2+a2−b2ca∣<2\left| \frac{c^2+a^2-b^2}{ca} \right| <2.
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