MathDB
Romania NMO 2023 Grade 8 P2

Source: Romania National Olympiad 2023

April 14, 2023
algebra

Problem Statement

Prove that:
a) There are infinitely many pairs (x,y)(x,y) of real numbers from the interval [0,3][0,\sqrt{3}] which satisfy the equation x3−y2+y3−x2=3x\sqrt{3-y^2}+y\sqrt{3-x^2}=3.
b) There do not exist any pairs (x,y)(x,y) of rational numbers from the interval [0,3][0,\sqrt{3}] that satisfy the equation x3−y2+y3−x2=3x\sqrt{3-y^2}+y\sqrt{3-x^2}=3.
Back to ProblemsView on AoPS