MathDB
Solving System of Symmetric Equations on Reals

Source: Mexico National Olympiad Mock Exam 2018 Problem 3

November 6, 2018
algebrasystem of equationsAlgebraic Manipulations

Problem Statement

Find all nn-tuples of real numbers (x1,x2,…,xn)(x_1, x_2, \dots, x_n) such that, for every index kk with 1≤k≤n1\leq k\leq n, the following holds:
xk2=∑i<ji,j≠kxixj x_k^2=\sum\limits_{\substack{i < j \\ i, j\neq k}} x_ix_j
Proposed by Oriol Solé
Back to ProblemsView on AoPS