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min max of F =(y-x)(x+4y) when x^2y^2 + xy + 1 = 3y^2

Source: Czech-Polish-Slovak Junior Match 2014, Team p6 CPSJ

March 23, 2020

inequalitiesalgebraminimummaximumminmax

Problem Statement

Determine the largest and smallest fractions

F = \frac{y-x}{x+4y}

if the real numbers

x

and

y

satisfy the equation

x^2y^2 + xy + 1 = 3y^2