MathDB
system x^3+mx−n = 0, &, nx^3−2m2x^2 −5mnx−2m^3−n^2 = 0

Source: Spanish Mathematical Olympiad 1995 P5

July 31, 2018
algebrasystem of equations

Problem Statement

Prove that if the equations x3+mx−n=0x^3+mx-n = 0 nx3−2m2x2−5mnx−2m3−n2=0nx^3-2m^2x^2 -5mnx-2m^3-n^2 = 0 have one root in common (n≠0n \ne 0), then the first equation has two equal roots, and find the roots of the equations in terms of nn.
Back to ProblemsView on AoPS