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absolute value, squares and roots in the same dish

Source: OMEC Ecuador National Olympiad Final Round 2023 N3 P1 day 1

November 5, 2024

absolute valuealgebra

Problem Statement

Find all reals

(a, b, c)

such that

\begin{cases}a^2+b^2+c^2=1\\ |a+b|=\sqrt{2}\end{cases}