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Geometric Inequality

Source: 2013 Thailand October Camp Algebra and Functional Equations Exam p2

March 8, 2022
geometric inequalitygeometryinequalities

Problem Statement

In a triangle ABCABC, let x=cos⁡A−B2,y=cos⁡B−C2,z=cos⁡C−A2x=\cos\frac{A-B}{2},y=\cos\frac{B-C}{2},z=\cos\frac{C-A}{2}. Prove that x4+y4+z2≤1+2x2y2z2.x^4+y^4+z^2\leq 1+2x^2y^2z^2.
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