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"Can we use jensen for the test" The problem:

Source: Indonesia National Math Olympiad 2021 Problem 4 (INAMO 2021/4)

November 8, 2021

inequalitiesalgebra

Problem Statement

Let

x,y

and

z

be positive reals such that

x + y + z = 3

. Prove that

2 \sqrt{x + \sqrt{y}} + 2 \sqrt{y + \sqrt{z}} + 2 \sqrt{z + \sqrt{x}} \le \sqrt{8 + x - y} + \sqrt{8 + y - z} + \sqrt{8 + z - x}