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Regional Olympiad - FBH 2017 Grade 10 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2017

September 19, 2018
equationalgebraroots

Problem Statement

If aa is real number such that x1x_1 and x2x_2, x1≠x2x_1\neq x_2 , are real numbers and roots of equation x2−x+a=0x_2-x+a=0. Prove that ∣x12−x22∣=1\mid {x_1}^2-{x_2}^2 \mid =1 iff ∣x13−x23∣=1\mid {x_1}^3-{x_2}^3 \mid =1
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