6

Part of 2014 Czech-Polish-Slovak Junior Match

Problems(1)

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

Determine the largest and smallest fractions

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

if the real numbers

x

y

satisfy the equation

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

inequalitiesalgebraminimummaximumminmax