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Prove (x-y)^{3}+(y-z)^{3}+(z-x)^{3}>0

Source: MTRP 2018 Class 11-Short Answer Type Question: Problem 1 :-

February 17, 2021
inequalities

Problem Statement

Let x,y,zx, y, z are real numbers such that x<y<z.x<y<z . Prove that (x−y)3+(y−z)3+(z−x)3>0 (x-y)^{3}+(y-z)^{3}+(z-x)^{3}>0
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