MathDB
x_3 + x_4 \in Q, x_3 x_4 \notin Q => x_1 + x_2 = x_3 + x_4

Source: Polish National Olympiad 2015 2nd round, p4

August 28, 2019
polynomialalgebraSumrationalirrational number

Problem Statement

Real numbers x1,x2,x3,x4x_1, x_2, x_3, x_4 are roots of the fourth degree polynomial W(x)W (x) with integer coefficients. Prove that if x3+x4x_3 + x_4 is a rational number and x3x4x_3x_4 is a irrational number, then x1+x2=x3+x4x_1 + x_2 = x_3 + x_4.
Back to ProblemsView on AoPS