MathDB
Junior Ballkan Mathematical Olympiad 2020, Problem 1

Source: Junior Ballkan Mathematical Olympiad 2020, Problem 1

September 11, 2020
algebrasystem of equationsJunior BalkanpolynomialJuniorJBMOjbmo2020

Problem Statement

Find all triples (a,b,c)(a,b,c) of real numbers such that the following system holds: {a+b+c=1a+1b+1ca2+b2+c2=1a2+1b2+1c2\begin{cases} a+b+c=\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \\a^2+b^2+c^2=\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\end{cases}
Proposed by Dorlir Ahmeti, Albania
Back to ProblemsView on AoPS