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Regional Olympiad - FBH 2009 Grade 10 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2009

September 28, 2018
Systemalgebraminimuminequalities

Problem Statement

Find minimal value of a∈Ra \in \mathbb{R} such that system x−1+y−1+z−1=a−1\sqrt{x-1}+\sqrt{y-1}+\sqrt{z-1}=a-1 x+1+y+1+z+1=a+1\sqrt{x+1}+\sqrt{y+1}+\sqrt{z+1}=a+1 has solution in set of real numbers
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