MathDB
b^2 = 4a(\sqrt{c} - 1), c^2 = 4b (\sqrt{a} - 1), a^2 = 4c(\sqrt{b} - 1)

Source: Mathematics Regional Olympiad of Mexico Northeast 2017 P6

September 21, 2022
algebrasystem of equations

Problem Statement

Find all triples of real numbers (a,b,c)(a, b, c) that satisfy the system of equations {b2=4a(c−1)c2=4b(a−1)a2=4c(b−1)\begin{cases} b^2 = 4a(\sqrt{c} - 1) \\ c^2 = 4b (\sqrt{a} - 1) \\ a^2 = 4c(\sqrt{b} - 1) \end{cases}
Back to ProblemsView on AoPS