Problem #PRU-116558

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)

Problem

The nonzero numbers \(a\), \(b\), \(c\) are such that every two of the three equations \(ax^{11} + bx^4 + c = 0\), \(bx^{11} + cx^4 + a = 0\), \(cx^{11} + ax^4 + b = 0\) have a common root. Prove that all three equations have a common root.