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function problem hiding behind a geometry problem

Source:

February 7, 2021
geometryanalytic geometrymonotonyfunction

Problem Statement

Let be a number x x and three positive numbers a,b,c a,b,c such that ax+bx=cx. a^x+b^x=c^x. Prove that ay,by,cy a^y,b^y,c^y are the lenghts of the sides of an obtuse triangle if and only if y<x<2y. y<x<2y.
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